{"as_of":"2026-08-09T14:07:00Z","caps":{"database_statements":6,"inbound":100,"outbound":100},"context_digest":"sha256:ce5c0224442152d97d65890a663275fad45e72f713d7c0c75845fd0aa02e1a65","coverage":[{"denominator":70,"lane":"reference_resolution","note":"Typed states for the displayed outbound observations.","records_observed":70,"source":"paper_references, paper_reference_links","source_observed_at":"2026-08-01T10:25:18.978284Z","state":"measured"},{"denominator":70,"lane":"standing_notices","note":"One-hop event checks from named stored sources.","records_observed":70,"source":"scholarly_work_events, retraction_status_cache","source_observed_at":"2026-08-09T06:31:02.800959+00:00","state":"measured"},{"denominator":0,"lane":"inbound_itemization","note":"Pith citing papers itemized under the disclosed page cap.","records_observed":0,"source":"paper_references, paper_reference_links","source_observed_at":null,"state":"measured"},{"denominator":1,"lane":"external_citation_measurements","note":"A source-named dated measurement, never combined with another source.","records_observed":0,"source":"cited_works","source_observed_at":null,"state":"measured"}],"external_citation_measurements":[],"inbound":[],"links":{"evidence":"/evidence","html":"/paper/2607.20279/citation-record","integrity":"/paper/2607.20279/integrity","json":"/paper/2607.20279/citation-record.json","paper":"/paper/2607.20279"},"outbound":[{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-01T10:25:11.652146Z","title":null,"venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2607.20279","last_updated":"2026-07-22T15:27:25Z","snapshot_observed_at":"2026-08-04T23:50:45.227058Z","submitted_at":"2026-07-22T15:27:25Z","title":"Random walks in Dirichlet random environment in dimension $d+1$","version":1},"reference_index":1,"source":"pdf_text","source_observed_at":"2026-08-01T10:25:11.652146Z"},"links":{"citing_paper":"/paper/2607.20279"},"observation_digest":"sha256:17499cebd92738fccf135195d5a306942d2274ca39620eb8bdd03450ab05024c","observation_id":"7bb57063-633d-46fe-aed6-dc3ab4978592","resolution":{"observed_at":"2026-08-01T10:25:11.652146Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-01T10:25:11.760562Z","title":"Moreover in general dimensiond, the random walk satisfies a local central limit theorem [24]","venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2607.20279","last_updated":"2026-07-22T15:27:25Z","snapshot_observed_at":"2026-08-04T23:50:45.227058Z","submitted_at":"2026-07-22T15:27:25Z","title":"Random walks in Dirichlet random environment in dimension $d+1$","version":1},"reference_index":2,"source":"pdf_text","source_observed_at":"2026-08-01T10:25:11.760562Z"},"links":{"citing_paper":"/paper/2607.20279"},"observation_digest":"sha256:c9a87cef6aa64e85b6eec1d6fa91ceef09927fd8b7bc41954253e1136142ace9","observation_id":"995b2b72-9a9b-4f87-a13a-8281c3d2e4b1","resolution":{"observed_at":"2026-08-01T10:25:11.760562Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-01T10:25:12.307193Z","title":"At least one of theu i is zero","venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2607.20279","last_updated":"2026-07-22T15:27:25Z","snapshot_observed_at":"2026-08-04T23:50:45.227058Z","submitted_at":"2026-07-22T15:27:25Z","title":"Random walks in Dirichlet random environment in dimension $d+1$","version":1},"reference_index":3,"source":"pdf_text","source_observed_at":"2026-08-01T10:25:12.307193Z"},"links":{"citing_paper":"/paper/2607.20279"},"observation_digest":"sha256:91afff68662b1e7cf4490eaa47eb5c8984453f50cf98ab383418000142443c43","observation_id":"8defa633-632f-4654-99c0-81eb5d3dda30","resolution":{"observed_at":"2026-08-01T10:25:12.307193Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-01T10:25:11.517667Z","title":"As a consequence, it was predicted that for anyv̸= 0 ind= 2, and forv >v c ind= 3, the fluctuations of logP(X(t) =tv) scale ast β at larget, whereβis the DP exponent in dimensiond","venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2607.20279","last_updated":"2026-07-22T15:27:25Z","snapshot_observed_at":"2026-08-04T23:50:45.227058Z","submitted_at":"2026-07-22T15:27:25Z","title":"Random walks in Dirichlet random environment in dimension $d+1$","version":1},"reference_index":4,"source":"pdf_text","source_observed_at":"2026-08-01T10:25:11.517667Z"},"links":{"citing_paper":"/paper/2607.20279"},"observation_digest":"sha256:58526f047bdd85ccb4b620e441132ba1bf94ea60b69232d04f24006c459370e3","observation_id":"20c19231-2d7a-4b35-b843-05410e589b28","resolution":{"observed_at":"2026-08-01T10:25:11.517667Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-01T10:25:11.990611Z","title":null,"venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2607.20279","last_updated":"2026-07-22T15:27:25Z","snapshot_observed_at":"2026-08-04T23:50:45.227058Z","submitted_at":"2026-07-22T15:27:25Z","title":"Random walks in Dirichlet random environment in dimension $d+1$","version":1},"reference_index":5,"source":"pdf_text","source_observed_at":"2026-08-01T10:25:11.990611Z"},"links":{"citing_paper":"/paper/2607.20279"},"observation_digest":"sha256:421ecf28a8c685fda949768e3634fca90f56c4e81026140c3755da8b20f15934","observation_id":"22bfdea1-1d6d-4ff6-b0a4-caccfcceec7f","resolution":{"observed_at":"2026-08-01T10:25:11.990611Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-01T10:25:12.188338Z","title":"The vectoru∈(R +)d+1 is chosen so thatu 1 + ···+u d+1 = 1,u̸=d","venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2607.20279","last_updated":"2026-07-22T15:27:25Z","snapshot_observed_at":"2026-08-04T23:50:45.227058Z","submitted_at":"2026-07-22T15:27:25Z","title":"Random walks in Dirichlet random environment in dimension $d+1$","version":1},"reference_index":6,"source":"pdf_text","source_observed_at":"2026-08-01T10:25:12.188338Z"},"links":{"citing_paper":"/paper/2607.20279"},"observation_digest":"sha256:6a57b7016c03aad5a00cebc370760771fe27d430df3105d1c96489ae54080a71","observation_id":"6ae5c82f-183d-404c-b1e7-7983a41e0efe","resolution":{"observed_at":"2026-08-01T10:25:12.188338Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-01T10:25:13.942483Z","title":"Corwin and Y","venue":null,"work_id":null,"year":2017},"citing_paper":{"arxiv_id":"2607.20279","last_updated":"2026-07-22T15:27:25Z","snapshot_observed_at":"2026-08-04T23:50:45.227058Z","submitted_at":"2026-07-22T15:27:25Z","title":"Random walks in Dirichlet random environment in dimension $d+1$","version":1},"reference_index":7,"source":"pdf_text","source_observed_at":"2026-08-01T10:25:13.942483Z"},"links":{"citing_paper":"/paper/2607.20279"},"observation_digest":"sha256:3ac8e536baf2ab56fdbd14275a1114e075163c921d98b677bfd3381701140018","observation_id":"79e30c24-a1e4-4f95-88c1-c10b1f3ebed1","resolution":{"observed_at":"2026-08-01T10:25:13.942483Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-01T10:25:12.491485Z","title":"3 for four vec- tors: the diagonalu=d= (1/2,1/2), off diagonal vectorsu= (2/3,1/3),u= (10/11,1/11) and an edge (1,0)","venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2607.20279","last_updated":"2026-07-22T15:27:25Z","snapshot_observed_at":"2026-08-04T23:50:45.227058Z","submitted_at":"2026-07-22T15:27:25Z","title":"Random walks in Dirichlet random environment in dimension $d+1$","version":1},"reference_index":8,"source":"pdf_text","source_observed_at":"2026-08-01T10:25:12.491485Z"},"links":{"citing_paper":"/paper/2607.20279"},"observation_digest":"sha256:0871092d1f6aaa8293d1973e1a7d77e999289d29711abde558ab5b2bafbe01b4","observation_id":"1e0b4f3a-0d8b-4687-9ea1-4a30d09894e4","resolution":{"observed_at":"2026-08-01T10:25:12.491485Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-01T10:25:12.694674Z","title":null,"venue":null,"work_id":null,"year":2000},"citing_paper":{"arxiv_id":"2607.20279","last_updated":"2026-07-22T15:27:25Z","snapshot_observed_at":"2026-08-04T23:50:45.227058Z","submitted_at":"2026-07-22T15:27:25Z","title":"Random walks in Dirichlet random environment in dimension $d+1$","version":1},"reference_index":9,"source":"pdf_text","source_observed_at":"2026-08-01T10:25:12.694674Z"},"links":{"citing_paper":"/paper/2607.20279"},"observation_digest":"sha256:cb8b38112903600f9c6e22ceb432b12131b4a861cab04dcf8a6d1fdead00120d","observation_id":"c4e3fbb1-cb75-4f46-acfa-a936554ef9ac","resolution":{"observed_at":"2026-08-01T10:25:12.694674Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-01T10:25:12.916474Z","title":"Our results are shown in Fig","venue":null,"work_id":null,"year":2000},"citing_paper":{"arxiv_id":"2607.20279","last_updated":"2026-07-22T15:27:25Z","snapshot_observed_at":"2026-08-04T23:50:45.227058Z","submitted_at":"2026-07-22T15:27:25Z","title":"Random walks in Dirichlet random environment in dimension $d+1$","version":1},"reference_index":10,"source":"pdf_text","source_observed_at":"2026-08-01T10:25:12.916474Z"},"links":{"citing_paper":"/paper/2607.20279"},"observation_digest":"sha256:0e1d20a32b6ad68fd75b0f6168543bef3dcbe23a768ccaec248f2c2fcab861e5","observation_id":"256adc29-f73b-4d71-8c7f-59d7072e695e","resolution":{"observed_at":"2026-08-01T10:25:12.916474Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-01T10:25:14.285857Z","title":"Parekh, arXiv:2401.06073 (2024)","venue":null,"work_id":null,"year":2024},"citing_paper":{"arxiv_id":"2607.20279","last_updated":"2026-07-22T15:27:25Z","snapshot_observed_at":"2026-08-04T23:50:45.227058Z","submitted_at":"2026-07-22T15:27:25Z","title":"Random walks in Dirichlet random environment in dimension $d+1$","version":1},"reference_index":11,"source":"pdf_text","source_observed_at":"2026-08-01T10:25:14.285857Z"},"links":{"citing_paper":"/paper/2607.20279"},"observation_digest":"sha256:3bac10e96b34d73db89c680206b5afd7f7ef6328e62e5548cae6986d58248d48","observation_id":"f494add9-10c9-42bb-82b4-81dd2f04e748","resolution":{"observed_at":"2026-08-01T10:25:14.285857Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-01T10:25:13.241197Z","title":"The sec- ond moment (Zt)2 is shown in Fig","venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2607.20279","last_updated":"2026-07-22T15:27:25Z","snapshot_observed_at":"2026-08-04T23:50:45.227058Z","submitted_at":"2026-07-22T15:27:25Z","title":"Random walks in Dirichlet random environment in dimension $d+1$","version":1},"reference_index":12,"source":"pdf_text","source_observed_at":"2026-08-01T10:25:13.241197Z"},"links":{"citing_paper":"/paper/2607.20279"},"observation_digest":"sha256:acb86cb69cf155c57f4af19f065afb19851241c17eb626ca9e0dbc36c9d4a594","observation_id":"d54694c7-ddb3-4f71-9b56-0a75f83f00fb","resolution":{"observed_at":"2026-08-01T10:25:13.241197Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-01T10:25:13.342693Z","title":"(36) and (37), both shown in Fig","venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2607.20279","last_updated":"2026-07-22T15:27:25Z","snapshot_observed_at":"2026-08-04T23:50:45.227058Z","submitted_at":"2026-07-22T15:27:25Z","title":"Random walks in Dirichlet random environment in dimension $d+1$","version":1},"reference_index":13,"source":"pdf_text","source_observed_at":"2026-08-01T10:25:13.342693Z"},"links":{"citing_paper":"/paper/2607.20279"},"observation_digest":"sha256:f401478dbb44b23cf94bd61c19f6ee343e4d3bf77309147e9f3fe19f71cda854","observation_id":"5aadb0b9-c190-4de7-a701-ce4620564073","resolution":{"observed_at":"2026-08-01T10:25:13.342693Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-01T10:25:13.431871Z","title":"Kardar, G","venue":null,"work_id":null,"year":1986},"citing_paper":{"arxiv_id":"2607.20279","last_updated":"2026-07-22T15:27:25Z","snapshot_observed_at":"2026-08-04T23:50:45.227058Z","submitted_at":"2026-07-22T15:27:25Z","title":"Random walks in Dirichlet random environment in dimension $d+1$","version":1},"reference_index":14,"source":"pdf_text","source_observed_at":"2026-08-01T10:25:13.431871Z"},"links":{"citing_paper":"/paper/2607.20279"},"observation_digest":"sha256:812d1b0eecdcde254682ec14423f63b10f31e37102afbccef59ee21424d0bbe9","observation_id":"d8cb44af-bcb2-42fc-827d-6e3c649ad8c9","resolution":{"observed_at":"2026-08-01T10:25:13.431871Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-01T10:25:13.529762Z","title":"Barraquand and I","venue":null,"work_id":null,"year":2017},"citing_paper":{"arxiv_id":"2607.20279","last_updated":"2026-07-22T15:27:25Z","snapshot_observed_at":"2026-08-04T23:50:45.227058Z","submitted_at":"2026-07-22T15:27:25Z","title":"Random walks in Dirichlet random environment in dimension $d+1$","version":1},"reference_index":15,"source":"pdf_text","source_observed_at":"2026-08-01T10:25:13.529762Z"},"links":{"citing_paper":"/paper/2607.20279"},"observation_digest":"sha256:cfc595aa9b4b2baa04a62bd812198d8adce012d8e740b06b1c58c9efc752cfcd","observation_id":"82baecf3-252e-4907-9720-4b7f1275f5ec","resolution":{"observed_at":"2026-08-01T10:25:13.529762Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-01T10:25:13.602812Z","title":null,"venue":null,"work_id":null,"year":1994},"citing_paper":{"arxiv_id":"2607.20279","last_updated":"2026-07-22T15:27:25Z","snapshot_observed_at":"2026-08-04T23:50:45.227058Z","submitted_at":"2026-07-22T15:27:25Z","title":"Random walks in Dirichlet random environment in dimension $d+1$","version":1},"reference_index":16,"source":"pdf_text","source_observed_at":"2026-08-01T10:25:13.602812Z"},"links":{"citing_paper":"/paper/2607.20279"},"observation_digest":"sha256:d229802c7128f12b1c97ae2c8d26dd16b4702f71c6c8bf836c9070ec7d937fdf","observation_id":"729b9eca-0fd2-493a-afaa-e0dd5f43b101","resolution":{"observed_at":"2026-08-01T10:25:13.602812Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-01T10:25:13.684339Z","title":"Le Doussal and T","venue":null,"work_id":null,"year":2017},"citing_paper":{"arxiv_id":"2607.20279","last_updated":"2026-07-22T15:27:25Z","snapshot_observed_at":"2026-08-04T23:50:45.227058Z","submitted_at":"2026-07-22T15:27:25Z","title":"Random walks in Dirichlet random environment in dimension $d+1$","version":1},"reference_index":17,"source":"pdf_text","source_observed_at":"2026-08-01T10:25:13.684339Z"},"links":{"citing_paper":"/paper/2607.20279"},"observation_digest":"sha256:ae7979e7cafe6dcfcbc89f2c6e480903b4b6e3612740ca7ccbfcc5c3413ef46f","observation_id":"8492641a-9a0a-49e1-84e5-606517024d62","resolution":{"observed_at":"2026-08-01T10:25:13.684339Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-01T10:25:13.748377Z","title":"Thiery and P","venue":null,"work_id":null,"year":2016},"citing_paper":{"arxiv_id":"2607.20279","last_updated":"2026-07-22T15:27:25Z","snapshot_observed_at":"2026-08-04T23:50:45.227058Z","submitted_at":"2026-07-22T15:27:25Z","title":"Random walks in Dirichlet random environment in dimension $d+1$","version":1},"reference_index":18,"source":"pdf_text","source_observed_at":"2026-08-01T10:25:13.748377Z"},"links":{"citing_paper":"/paper/2607.20279"},"observation_digest":"sha256:563df711ae4c105d39846a9729fd7445ac5570e3378d67e2fc310f457ef84ba3","observation_id":"d96df5a5-c05b-44c4-beb8-ea602754d780","resolution":{"observed_at":"2026-08-01T10:25:13.748377Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-01T10:25:13.874966Z","title":"Barraquand and P","venue":null,"work_id":null,"year":2020},"citing_paper":{"arxiv_id":"2607.20279","last_updated":"2026-07-22T15:27:25Z","snapshot_observed_at":"2026-08-04T23:50:45.227058Z","submitted_at":"2026-07-22T15:27:25Z","title":"Random walks in Dirichlet random environment in dimension $d+1$","version":1},"reference_index":19,"source":"pdf_text","source_observed_at":"2026-08-01T10:25:13.874966Z"},"links":{"citing_paper":"/paper/2607.20279"},"observation_digest":"sha256:1926a50168b45024ce7999d41b8173c38ba930ef07bbec8a8bde45e0f6806db1","observation_id":"d73396c3-b4dc-497f-b7ca-d7c004b5cce0","resolution":{"observed_at":"2026-08-01T10:25:13.874966Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2502.04113","last_updated":"2025-11-10T14:08:13Z","snapshot_observed_at":"2026-07-06T20:32:14.203915Z","submitted_at":"2025-02-06T14:40:33Z","title":"Coincidence of critical points for directed polymers for general environments and random walks","version":2},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2502.04113","snapshot_observed_at":"2026-08-01T10:25:15.098454Z","title":"Junk and H","venue":null,"work_id":null,"year":2025},"citing_paper":{"arxiv_id":"2607.20279","last_updated":"2026-07-22T15:27:25Z","snapshot_observed_at":"2026-08-04T23:50:45.227058Z","submitted_at":"2026-07-22T15:27:25Z","title":"Random walks in Dirichlet random environment in dimension $d+1$","version":1},"reference_index":20,"source":"pdf_text","source_observed_at":"2026-08-01T10:25:15.098454Z"},"links":{"cited_paper":"/paper/2502.04113","citing_paper":"/paper/2607.20279"},"observation_digest":"sha256:4f2a246271187638d5efbbb2e805c3fc26704ad812d2b90488204bafa5740c6b","observation_id":"ee65ab15-0b54-4310-8070-809b61828b10","resolution":{"observed_at":"2026-08-01T10:25:15.098454Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-01T10:25:11.560737Z","title":null,"venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2607.20279","last_updated":"2026-07-22T15:27:25Z","snapshot_observed_at":"2026-08-04T23:50:45.227058Z","submitted_at":"2026-07-22T15:27:25Z","title":"Random walks in Dirichlet random environment in dimension $d+1$","version":1},"reference_index":21,"source":"pdf_text","source_observed_at":"2026-08-01T10:25:11.560737Z"},"links":{"citing_paper":"/paper/2607.20279"},"observation_digest":"sha256:74d3810ff7637c6acc54f4089713f56a534ee81f6ff67e41851f03ba4af3b710","observation_id":"827f322a-32af-4815-83d6-2c5911c7c824","resolution":{"observed_at":"2026-08-01T10:25:11.560737Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"1905.10280","last_updated":"2020-10-08T16:44:45Z","snapshot_observed_at":"2026-08-05T18:57:43.968940Z","submitted_at":"2019-05-24T15:21:40Z","title":"Large Deviations For Sticky Brownian Motions","version":3},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"1905.10280","snapshot_observed_at":"2026-08-01T10:25:14.046819Z","title":"Barraquand and M","venue":null,"work_id":null,"year":2020},"citing_paper":{"arxiv_id":"2607.20279","last_updated":"2026-07-22T15:27:25Z","snapshot_observed_at":"2026-08-04T23:50:45.227058Z","submitted_at":"2026-07-22T15:27:25Z","title":"Random walks in Dirichlet random environment in dimension $d+1$","version":1},"reference_index":22,"source":"pdf_text","source_observed_at":"2026-08-01T10:25:14.046819Z"},"links":{"cited_paper":"/paper/1905.10280","citing_paper":"/paper/2607.20279"},"observation_digest":"sha256:cc420a0a6ff3a934f67355a5899ff5167e060bc10fdb893b022bfaaa65357831","observation_id":"9b464d20-a5ae-4092-82f4-ba5c795b62c9","resolution":{"observed_at":"2026-08-01T10:25:14.046819Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-01T10:25:14.153587Z","title":null,"venue":null,"work_id":null,"year":2024},"citing_paper":{"arxiv_id":"2607.20279","last_updated":"2026-07-22T15:27:25Z","snapshot_observed_at":"2026-08-04T23:50:45.227058Z","submitted_at":"2026-07-22T15:27:25Z","title":"Random walks in Dirichlet random environment in dimension $d+1$","version":1},"reference_index":23,"source":"pdf_text","source_observed_at":"2026-08-01T10:25:14.153587Z"},"links":{"citing_paper":"/paper/2607.20279"},"observation_digest":"sha256:047449fbeea192fd0e60d79880baab11bee93add0b4f4a821f10fe741a79db27","observation_id":"0d0f78fd-6d3f-4e60-9c65-3d46e4fdd8fb","resolution":{"observed_at":"2026-08-01T10:25:14.153587Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2304.14279","last_updated":"2024-12-21T16:08:55Z","snapshot_observed_at":"2026-07-06T15:20:49.723743Z","submitted_at":"2023-04-27T15:40:34Z","title":"KPZ equation limit of sticky Brownian motion","version":3},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2304.14279","snapshot_observed_at":"2026-08-01T10:25:14.217114Z","title":null,"venue":null,"work_id":null,"year":2024},"citing_paper":{"arxiv_id":"2607.20279","last_updated":"2026-07-22T15:27:25Z","snapshot_observed_at":"2026-08-04T23:50:45.227058Z","submitted_at":"2026-07-22T15:27:25Z","title":"Random walks in Dirichlet random environment in dimension $d+1$","version":1},"reference_index":24,"source":"pdf_text","source_observed_at":"2026-08-01T10:25:14.217114Z"},"links":{"cited_paper":"/paper/2304.14279","citing_paper":"/paper/2607.20279"},"observation_digest":"sha256:71ab29aad4414875ae614dba167ba15e411244cf858605a3fc855f682deb0eae","observation_id":"5dc699b8-98d2-4967-a843-873fc704cb4a","resolution":{"observed_at":"2026-08-01T10:25:14.217114Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2507.19222","last_updated":"2025-08-25T07:15:56Z","snapshot_observed_at":"2026-08-06T14:24:41.386225Z","submitted_at":"2025-07-25T12:43:31Z","title":"Convergence of the KMP model to the KPZ equation","version":2},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2507.19222","snapshot_observed_at":"2026-08-01T10:25:14.347779Z","title":"Barraquand and F","venue":null,"work_id":null,"year":2025},"citing_paper":{"arxiv_id":"2607.20279","last_updated":"2026-07-22T15:27:25Z","snapshot_observed_at":"2026-08-04T23:50:45.227058Z","submitted_at":"2026-07-22T15:27:25Z","title":"Random walks in Dirichlet random environment in dimension $d+1$","version":1},"reference_index":25,"source":"pdf_text","source_observed_at":"2026-08-01T10:25:14.347779Z"},"links":{"cited_paper":"/paper/2507.19222","citing_paper":"/paper/2607.20279"},"observation_digest":"sha256:b713128f6a9bf54085d4f40bd37b86b106edaae52e4fc44ceeeace93b4e317d2","observation_id":"2b3f6ec8-1d9d-4970-8d7c-aff0c2f63dc6","resolution":{"observed_at":"2026-08-01T10:25:14.347779Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-01T10:25:14.416106Z","title":null,"venue":null,"work_id":null,"year":2023},"citing_paper":{"arxiv_id":"2607.20279","last_updated":"2026-07-22T15:27:25Z","snapshot_observed_at":"2026-08-04T23:50:45.227058Z","submitted_at":"2026-07-22T15:27:25Z","title":"Random walks in Dirichlet random environment in dimension $d+1$","version":1},"reference_index":26,"source":"pdf_text","source_observed_at":"2026-08-01T10:25:14.416106Z"},"links":{"citing_paper":"/paper/2607.20279"},"observation_digest":"sha256:49529712713c2e2281fbf5c168e6e742da668cbc50a34c69a59bafd208c768d2","observation_id":"9d89b66a-964c-4ad8-b868-0d14ed9ef3cf","resolution":{"observed_at":"2026-08-01T10:25:14.416106Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-01T10:25:14.510114Z","title":null,"venue":null,"work_id":null,"year":2024},"citing_paper":{"arxiv_id":"2607.20279","last_updated":"2026-07-22T15:27:25Z","snapshot_observed_at":"2026-08-04T23:50:45.227058Z","submitted_at":"2026-07-22T15:27:25Z","title":"Random walks in Dirichlet random environment in dimension $d+1$","version":1},"reference_index":27,"source":"pdf_text","source_observed_at":"2026-08-01T10:25:14.510114Z"},"links":{"citing_paper":"/paper/2607.20279"},"observation_digest":"sha256:c313390ff2ca0dc335bc61e45537f9f91134f55492b927c2ab704263c50a7f4d","observation_id":"bddf118e-43af-441e-9a45-3d4203d8f5f5","resolution":{"observed_at":"2026-08-01T10:25:14.510114Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-01T10:25:14.656380Z","title":null,"venue":null,"work_id":null,"year":2024},"citing_paper":{"arxiv_id":"2607.20279","last_updated":"2026-07-22T15:27:25Z","snapshot_observed_at":"2026-08-04T23:50:45.227058Z","submitted_at":"2026-07-22T15:27:25Z","title":"Random walks in Dirichlet random environment in dimension $d+1$","version":1},"reference_index":28,"source":"pdf_text","source_observed_at":"2026-08-01T10:25:14.656380Z"},"links":{"citing_paper":"/paper/2607.20279"},"observation_digest":"sha256:deae36f3c51c2391c67966ff27d6e1ed5231248837d9f6d99f4c29289598f4a5","observation_id":"4ab3d276-d28f-4f7d-a52b-0a735a36a11c","resolution":{"observed_at":"2026-08-01T10:25:14.656380Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2505.01533","last_updated":"2025-05-02T18:37:37Z","snapshot_observed_at":"2026-08-09T07:15:02.962031Z","submitted_at":"2025-05-02T18:37:37Z","title":"Super-Universal Behavior of Outliers Diffusing in a Space-Time Random Environment","version":1},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2505.01533","snapshot_observed_at":"2026-08-01T10:25:14.747265Z","title":"Hass, arXiv preprint arXiv:2505.01533 (2025)","venue":null,"work_id":null,"year":2025},"citing_paper":{"arxiv_id":"2607.20279","last_updated":"2026-07-22T15:27:25Z","snapshot_observed_at":"2026-08-04T23:50:45.227058Z","submitted_at":"2026-07-22T15:27:25Z","title":"Random walks in Dirichlet random environment in dimension $d+1$","version":1},"reference_index":29,"source":"pdf_text","source_observed_at":"2026-08-01T10:25:14.747265Z"},"links":{"cited_paper":"/paper/2505.01533","citing_paper":"/paper/2607.20279"},"observation_digest":"sha256:22850ad1d20157e1378a87b19eed565f89db607299e6774551dd2b323687bb2c","observation_id":"10f0f37e-ff96-413a-a3e3-34b46d46383c","resolution":{"observed_at":"2026-08-01T10:25:14.747265Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2504.00266","last_updated":"2025-03-31T22:18:37Z","snapshot_observed_at":"2026-08-08T23:45:35.471348Z","submitted_at":"2025-03-31T22:18:37Z","title":"Universal KPZ Fluctuations for Moderate Deviations of Random Walks in Random Environments","version":1},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2504.00266","snapshot_observed_at":"2026-08-01T10:25:14.840668Z","title":null,"venue":null,"work_id":null,"year":2025},"citing_paper":{"arxiv_id":"2607.20279","last_updated":"2026-07-22T15:27:25Z","snapshot_observed_at":"2026-08-04T23:50:45.227058Z","submitted_at":"2026-07-22T15:27:25Z","title":"Random walks in Dirichlet random environment in dimension $d+1$","version":1},"reference_index":30,"source":"pdf_text","source_observed_at":"2026-08-01T10:25:14.840668Z"},"links":{"cited_paper":"/paper/2504.00266","citing_paper":"/paper/2607.20279"},"observation_digest":"sha256:9418400815c0dc2b62e0fbde30e152bbba45e16c61ae23f40fbc9891af2c6980","observation_id":"7bdcc2a6-a794-40a8-b90f-aa91183c147b","resolution":{"observed_at":"2026-08-01T10:25:14.840668Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-01T10:25:14.929960Z","title":"Monthus and T","venue":null,"work_id":null,"year":2006},"citing_paper":{"arxiv_id":"2607.20279","last_updated":"2026-07-22T15:27:25Z","snapshot_observed_at":"2026-08-04T23:50:45.227058Z","submitted_at":"2026-07-22T15:27:25Z","title":"Random walks in Dirichlet random environment in dimension $d+1$","version":1},"reference_index":31,"source":"pdf_text","source_observed_at":"2026-08-01T10:25:14.929960Z"},"links":{"citing_paper":"/paper/2607.20279"},"observation_digest":"sha256:40f30f34ce795e6004f70a22e45bf970b2b7fd374fd10c561846c45f668f0a8a","observation_id":"a4d920c4-7066-4b09-b385-38e8f3e17efb","resolution":{"observed_at":"2026-08-01T10:25:14.929960Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-01T10:25:15.010681Z","title":"Junk and H","venue":null,"work_id":null,"year":2024},"citing_paper":{"arxiv_id":"2607.20279","last_updated":"2026-07-22T15:27:25Z","snapshot_observed_at":"2026-08-04T23:50:45.227058Z","submitted_at":"2026-07-22T15:27:25Z","title":"Random walks in Dirichlet random environment in dimension $d+1$","version":1},"reference_index":32,"source":"pdf_text","source_observed_at":"2026-08-01T10:25:15.010681Z"},"links":{"citing_paper":"/paper/2607.20279"},"observation_digest":"sha256:d7c35885031ad26c3f6a73be1d6898eb47fb4c995f9aa09fa913bc369e12318a","observation_id":"7e6412c0-631b-4f73-b516-2bb3b4f1c6c6","resolution":{"observed_at":"2026-08-01T10:25:15.010681Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-01T10:25:16.252956Z","title":"Pagnani and G","venue":null,"work_id":null,"year":2015},"citing_paper":{"arxiv_id":"2607.20279","last_updated":"2026-07-22T15:27:25Z","snapshot_observed_at":"2026-08-04T23:50:45.227058Z","submitted_at":"2026-07-22T15:27:25Z","title":"Random walks in Dirichlet random environment in dimension $d+1$","version":1},"reference_index":33,"source":"pdf_text","source_observed_at":"2026-08-01T10:25:16.252956Z"},"links":{"citing_paper":"/paper/2607.20279"},"observation_digest":"sha256:46aec60e802f54b2f9a86a44108b1dc5f3f3dfc3903eb4553f1227db89af9381","observation_id":"e9d184bb-6be3-4408-aec3-62e2c317401d","resolution":{"observed_at":"2026-08-01T10:25:16.252956Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-01T10:25:15.165649Z","title":"Drillick and S","venue":null,"work_id":null,"year":2025},"citing_paper":{"arxiv_id":"2607.20279","last_updated":"2026-07-22T15:27:25Z","snapshot_observed_at":"2026-08-04T23:50:45.227058Z","submitted_at":"2026-07-22T15:27:25Z","title":"Random walks in Dirichlet random environment in dimension $d+1$","version":1},"reference_index":34,"source":"pdf_text","source_observed_at":"2026-08-01T10:25:15.165649Z"},"links":{"citing_paper":"/paper/2607.20279"},"observation_digest":"sha256:36ac6e9da929a29d0bba7dc71b444470572099e2f71f459a8b812f5eb679af98","observation_id":"e6b65061-1be6-487c-9ac6-1e9ae89a727d","resolution":{"observed_at":"2026-08-01T10:25:15.165649Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2508.15999","last_updated":"2025-08-21T23:19:32Z","snapshot_observed_at":"2026-08-05T17:37:32.565799Z","submitted_at":"2025-08-21T23:19:32Z","title":"Universal Fluctuations in the Tail Probability for d=2 Random Walks in Space-Time Random Environments","version":1},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2508.15999","snapshot_observed_at":"2026-08-01T10:25:15.253244Z","title":null,"venue":null,"work_id":null,"year":2025},"citing_paper":{"arxiv_id":"2607.20279","last_updated":"2026-07-22T15:27:25Z","snapshot_observed_at":"2026-08-04T23:50:45.227058Z","submitted_at":"2026-07-22T15:27:25Z","title":"Random walks in Dirichlet random environment in dimension $d+1$","version":1},"reference_index":35,"source":"pdf_text","source_observed_at":"2026-08-01T10:25:15.253244Z"},"links":{"cited_paper":"/paper/2508.15999","citing_paper":"/paper/2607.20279"},"observation_digest":"sha256:fa94d1122e49ce8c71b0a4304907020c7283443717a3610c49cfeef40f696d9b","observation_id":"b442c4de-1816-4e17-b45e-1a29536fdd56","resolution":{"observed_at":"2026-08-01T10:25:15.253244Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-01T10:25:15.310438Z","title":"Rassoul-Agha and T","venue":null,"work_id":null,"year":2005},"citing_paper":{"arxiv_id":"2607.20279","last_updated":"2026-07-22T15:27:25Z","snapshot_observed_at":"2026-08-04T23:50:45.227058Z","submitted_at":"2026-07-22T15:27:25Z","title":"Random walks in Dirichlet random environment in dimension $d+1$","version":1},"reference_index":36,"source":"pdf_text","source_observed_at":"2026-08-01T10:25:15.310438Z"},"links":{"citing_paper":"/paper/2607.20279"},"observation_digest":"sha256:f2286458ee8a4681ebd7a2c51eb058d5a6d35f8acf557f1ff5bb06799ace8af4","observation_id":"d68c73ef-fc16-44e5-b256-3297ea96cba8","resolution":{"observed_at":"2026-08-01T10:25:15.310438Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-01T10:25:15.410514Z","title":"Boldrighini, R","venue":null,"work_id":null,"year":1997},"citing_paper":{"arxiv_id":"2607.20279","last_updated":"2026-07-22T15:27:25Z","snapshot_observed_at":"2026-08-04T23:50:45.227058Z","submitted_at":"2026-07-22T15:27:25Z","title":"Random walks in Dirichlet random environment in dimension $d+1$","version":1},"reference_index":37,"source":"pdf_text","source_observed_at":"2026-08-01T10:25:15.410514Z"},"links":{"citing_paper":"/paper/2607.20279"},"observation_digest":"sha256:f17e3782fc9fc369d9bae7cc3ee8bbd2f99a347236ff5d3a82ec3d4794a32c82","observation_id":"290264d7-e4c2-4f7f-8155-903be8500be5","resolution":{"observed_at":"2026-08-01T10:25:15.410514Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"1104.3110","last_updated":"2011-12-14T18:09:46Z","snapshot_observed_at":"2026-08-03T22:16:34.188801Z","submitted_at":"2011-04-15T16:44:32Z","title":"Quenched Free Energy and Large Deviations for Random Walks in Random Potentials","version":2},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"1104.3110","snapshot_observed_at":"2026-08-01T10:25:15.463163Z","title":"Rassoul-Agha, T","venue":null,"work_id":null,"year":2013},"citing_paper":{"arxiv_id":"2607.20279","last_updated":"2026-07-22T15:27:25Z","snapshot_observed_at":"2026-08-04T23:50:45.227058Z","submitted_at":"2026-07-22T15:27:25Z","title":"Random walks in Dirichlet random environment in dimension $d+1$","version":1},"reference_index":38,"source":"pdf_text","source_observed_at":"2026-08-01T10:25:15.463163Z"},"links":{"cited_paper":"/paper/1104.3110","citing_paper":"/paper/2607.20279"},"observation_digest":"sha256:2260780b9a4c33a4a39709b801af7d705bd7217256ab4cd9a0c68d3f1f3efb20","observation_id":"49d814fe-aeab-4c64-8d72-d173d0542844","resolution":{"observed_at":"2026-08-01T10:25:15.463163Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-01T10:25:15.605403Z","title":"Korotkikh, Probability Theory and Related Fields184, 493 (2022)","venue":null,"work_id":null,"year":2022},"citing_paper":{"arxiv_id":"2607.20279","last_updated":"2026-07-22T15:27:25Z","snapshot_observed_at":"2026-08-04T23:50:45.227058Z","submitted_at":"2026-07-22T15:27:25Z","title":"Random walks in Dirichlet random environment in dimension $d+1$","version":1},"reference_index":39,"source":"pdf_text","source_observed_at":"2026-08-01T10:25:15.605403Z"},"links":{"citing_paper":"/paper/2607.20279"},"observation_digest":"sha256:f126c533e3d2931235ac0a758e00f79bd1096ecb76e0e843b1cfc52e73893e8c","observation_id":"4bcb3d28-1cf4-4449-b2ad-a2e929d14495","resolution":{"observed_at":"2026-08-01T10:25:15.605403Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2204.04720","last_updated":"2022-04-10T16:34:54Z","snapshot_observed_at":"2026-07-06T12:58:42.245234Z","submitted_at":"2022-04-10T16:34:54Z","title":"The crossover from the Macroscopic Fluctuation Theory to the Kardar-Parisi-Zhang equation controls the large deviations beyond Einstein's diffusion","version":1},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2204.04720","snapshot_observed_at":"2026-08-01T10:25:15.705756Z","title":"Krajenbrink and P","venue":null,"work_id":null,"year":2023},"citing_paper":{"arxiv_id":"2607.20279","last_updated":"2026-07-22T15:27:25Z","snapshot_observed_at":"2026-08-04T23:50:45.227058Z","submitted_at":"2026-07-22T15:27:25Z","title":"Random walks in Dirichlet random environment in dimension $d+1$","version":1},"reference_index":40,"source":"pdf_text","source_observed_at":"2026-08-01T10:25:15.705756Z"},"links":{"cited_paper":"/paper/2204.04720","citing_paper":"/paper/2607.20279"},"observation_digest":"sha256:70806fbd41d151725ebdd0eee265b2d2b2ef72e8a5ccd3fc144d447b67f1ac3c","observation_id":"a942c98d-4b11-47e2-970e-c4e8244e0a8f","resolution":{"observed_at":"2026-08-01T10:25:15.705756Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2307.15041","last_updated":"2023-07-27T17:47:08Z","snapshot_observed_at":"2026-08-04T05:38:50.093892Z","submitted_at":"2023-07-27T17:47:08Z","title":"Probing the large deviations for the Beta random walk in random medium","version":1},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2307.15041","snapshot_observed_at":"2026-08-01T10:25:15.767353Z","title":null,"venue":null,"work_id":null,"year":2024},"citing_paper":{"arxiv_id":"2607.20279","last_updated":"2026-07-22T15:27:25Z","snapshot_observed_at":"2026-08-04T23:50:45.227058Z","submitted_at":"2026-07-22T15:27:25Z","title":"Random walks in Dirichlet random environment in dimension $d+1$","version":1},"reference_index":41,"source":"pdf_text","source_observed_at":"2026-08-01T10:25:15.767353Z"},"links":{"cited_paper":"/paper/2307.15041","citing_paper":"/paper/2607.20279"},"observation_digest":"sha256:67bfc4e722cf4e8df875923ccc25d6a7419083a2904f7b1ff3caf9db60337632","observation_id":"e93e37fc-0ee6-480d-960e-1d0160805e59","resolution":{"observed_at":"2026-08-01T10:25:15.767353Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-01T10:25:13.115309Z","title":null,"venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2607.20279","last_updated":"2026-07-22T15:27:25Z","snapshot_observed_at":"2026-08-04T23:50:45.227058Z","submitted_at":"2026-07-22T15:27:25Z","title":"Random walks in Dirichlet random environment in dimension $d+1$","version":1},"reference_index":42,"source":"pdf_text","source_observed_at":"2026-08-01T10:25:13.115309Z"},"links":{"citing_paper":"/paper/2607.20279"},"observation_digest":"sha256:2d08cef9dac8fec148d786d3979b42f748f9120ce2bf75ff16e44cb42f529a2f","observation_id":"2271d64a-4b9c-4858-8182-ada695eacdb4","resolution":{"observed_at":"2026-08-01T10:25:13.115309Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-01T10:25:15.853111Z","title":null,"venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2607.20279","last_updated":"2026-07-22T15:27:25Z","snapshot_observed_at":"2026-08-04T23:50:45.227058Z","submitted_at":"2026-07-22T15:27:25Z","title":"Random walks in Dirichlet random environment in dimension $d+1$","version":1},"reference_index":43,"source":"pdf_text","source_observed_at":"2026-08-01T10:25:15.853111Z"},"links":{"citing_paper":"/paper/2607.20279"},"observation_digest":"sha256:119e2c31c8b7ee7cc2087145e7b79edb64d951ff76029b16f250dca647c1b576","observation_id":"ada06a9a-af5a-4bfe-bfdd-fb687c8b4c64","resolution":{"observed_at":"2026-08-01T10:25:15.853111Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-01T10:25:15.955635Z","title":"Barraquand and M","venue":null,"work_id":null,"year":2023},"citing_paper":{"arxiv_id":"2607.20279","last_updated":"2026-07-22T15:27:25Z","snapshot_observed_at":"2026-08-04T23:50:45.227058Z","submitted_at":"2026-07-22T15:27:25Z","title":"Random walks in Dirichlet random environment in dimension $d+1$","version":1},"reference_index":44,"source":"pdf_text","source_observed_at":"2026-08-01T10:25:15.955635Z"},"links":{"citing_paper":"/paper/2607.20279"},"observation_digest":"sha256:98d340ceb5448d86594a892e1ea6ddf3081bf42218a4727fde5f05b5519eb11d","observation_id":"752d568b-64e6-4c9c-a692-13b14c9e1586","resolution":{"observed_at":"2026-08-01T10:25:15.955635Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-01T10:25:16.058098Z","title":null,"venue":null,"work_id":null,"year":1962},"citing_paper":{"arxiv_id":"2607.20279","last_updated":"2026-07-22T15:27:25Z","snapshot_observed_at":"2026-08-04T23:50:45.227058Z","submitted_at":"2026-07-22T15:27:25Z","title":"Random walks in Dirichlet random environment in dimension $d+1$","version":1},"reference_index":45,"source":"pdf_text","source_observed_at":"2026-08-01T10:25:16.058098Z"},"links":{"citing_paper":"/paper/2607.20279"},"observation_digest":"sha256:409f35af39254a5f20f5fc4fad55d3f2923e932eafc27c10bcdd2673acd25ad5","observation_id":"19653c7f-6a5d-4335-8946-edc4d94a618e","resolution":{"observed_at":"2026-08-01T10:25:16.058098Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-01T10:25:16.154414Z","title":null,"venue":null,"work_id":null,"year":1992},"citing_paper":{"arxiv_id":"2607.20279","last_updated":"2026-07-22T15:27:25Z","snapshot_observed_at":"2026-08-04T23:50:45.227058Z","submitted_at":"2026-07-22T15:27:25Z","title":"Random walks in Dirichlet random environment in dimension $d+1$","version":1},"reference_index":46,"source":"pdf_text","source_observed_at":"2026-08-01T10:25:16.154414Z"},"links":{"citing_paper":"/paper/2607.20279"},"observation_digest":"sha256:6c1436e12c34bfe53d837355805606677cf3308853205dbebcd5b5af9ff0e316","observation_id":"a5159867-51d3-476b-939f-fc8db146c9b7","resolution":{"observed_at":"2026-08-01T10:25:16.154414Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-01T10:25:16.369544Z","title":"´Odor, B","venue":null,"work_id":null,"year":2010},"citing_paper":{"arxiv_id":"2607.20279","last_updated":"2026-07-22T15:27:25Z","snapshot_observed_at":"2026-08-04T23:50:45.227058Z","submitted_at":"2026-07-22T15:27:25Z","title":"Random walks in Dirichlet random environment in dimension $d+1$","version":1},"reference_index":47,"source":"pdf_text","source_observed_at":"2026-08-01T10:25:16.369544Z"},"links":{"citing_paper":"/paper/2607.20279"},"observation_digest":"sha256:8e9b2e9902e0175ac29ea46c2c42d4ed61f6f051fe3d6583351b5da17f6d4482","observation_id":"da0b3e02-eded-49a3-8f21-e759a233e3be","resolution":{"observed_at":"2026-08-01T10:25:16.369544Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-01T10:25:16.469834Z","title":null,"venue":null,"work_id":null,"year":2015},"citing_paper":{"arxiv_id":"2607.20279","last_updated":"2026-07-22T15:27:25Z","snapshot_observed_at":"2026-08-04T23:50:45.227058Z","submitted_at":"2026-07-22T15:27:25Z","title":"Random walks in Dirichlet random environment in dimension $d+1$","version":1},"reference_index":48,"source":"pdf_text","source_observed_at":"2026-08-01T10:25:16.469834Z"},"links":{"citing_paper":"/paper/2607.20279"},"observation_digest":"sha256:8e48cc13f308b5b941a1b10aa4757dfb43b19d015de303ffe7a1457b521b2c51","observation_id":"37973a72-e6ef-45cc-8943-e529b8f050b7","resolution":{"observed_at":"2026-08-01T10:25:16.469834Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-01T10:25:16.531938Z","title":"Forster, D","venue":null,"work_id":null,"year":1977},"citing_paper":{"arxiv_id":"2607.20279","last_updated":"2026-07-22T15:27:25Z","snapshot_observed_at":"2026-08-04T23:50:45.227058Z","submitted_at":"2026-07-22T15:27:25Z","title":"Random walks in Dirichlet random environment in dimension $d+1$","version":1},"reference_index":49,"source":"pdf_text","source_observed_at":"2026-08-01T10:25:16.531938Z"},"links":{"citing_paper":"/paper/2607.20279"},"observation_digest":"sha256:45be0d178ec3bffdf349409a3e31db27c7746045fefbdafad238d3ef0356a8ed","observation_id":"23943a5a-d94a-4edd-bc70-9a0bdc35710b","resolution":{"observed_at":"2026-08-01T10:25:16.531938Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-01T10:25:16.688323Z","title":null,"venue":null,"work_id":null,"year":1985},"citing_paper":{"arxiv_id":"2607.20279","last_updated":"2026-07-22T15:27:25Z","snapshot_observed_at":"2026-08-04T23:50:45.227058Z","submitted_at":"2026-07-22T15:27:25Z","title":"Random walks in Dirichlet random environment in dimension $d+1$","version":1},"reference_index":50,"source":"pdf_text","source_observed_at":"2026-08-01T10:25:16.688323Z"},"links":{"citing_paper":"/paper/2607.20279"},"observation_digest":"sha256:ccbb3cb1229c774e035466d5d71ee5fbbb7a697af5cba336394bcbd90bc8058b","observation_id":"540b8dc7-a824-44ae-897f-a8b40865b391","resolution":{"observed_at":"2026-08-01T10:25:16.688323Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-01T10:25:16.852373Z","title":null,"venue":null,"work_id":null,"year":1999},"citing_paper":{"arxiv_id":"2607.20279","last_updated":"2026-07-22T15:27:25Z","snapshot_observed_at":"2026-08-04T23:50:45.227058Z","submitted_at":"2026-07-22T15:27:25Z","title":"Random walks in Dirichlet random environment in dimension $d+1$","version":1},"reference_index":51,"source":"pdf_text","source_observed_at":"2026-08-01T10:25:16.852373Z"},"links":{"citing_paper":"/paper/2607.20279"},"observation_digest":"sha256:8cdb8ef37197f7309b6b545404d46bfd1db07b29209bf8c594857b964e926199","observation_id":"bd3f5dc2-e230-4058-a5fb-8fe0f4c173d8","resolution":{"observed_at":"2026-08-01T10:25:16.852373Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-01T10:25:17.059614Z","title":"Marinari, A","venue":null,"work_id":null,"year":2000},"citing_paper":{"arxiv_id":"2607.20279","last_updated":"2026-07-22T15:27:25Z","snapshot_observed_at":"2026-08-04T23:50:45.227058Z","submitted_at":"2026-07-22T15:27:25Z","title":"Random walks in Dirichlet random environment in dimension $d+1$","version":1},"reference_index":52,"source":"pdf_text","source_observed_at":"2026-08-01T10:25:17.059614Z"},"links":{"citing_paper":"/paper/2607.20279"},"observation_digest":"sha256:85cbeb7b6e2c54ca0dec453f8402a491db4d0346558c3586fb1e4ef8fe7247d0","observation_id":"f55772ff-6ff4-48e7-90f1-737ed912d006","resolution":{"observed_at":"2026-08-01T10:25:17.059614Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-01T10:25:17.232022Z","title":null,"venue":null,"work_id":null,"year":2018},"citing_paper":{"arxiv_id":"2607.20279","last_updated":"2026-07-22T15:27:25Z","snapshot_observed_at":"2026-08-04T23:50:45.227058Z","submitted_at":"2026-07-22T15:27:25Z","title":"Random walks in Dirichlet random environment in dimension $d+1$","version":1},"reference_index":53,"source":"pdf_text","source_observed_at":"2026-08-01T10:25:17.232022Z"},"links":{"citing_paper":"/paper/2607.20279"},"observation_digest":"sha256:297bd5f4119bd9d795e62e2c5692691ba8a32b15acba9f03a4fbba958edd095f","observation_id":"41b442dd-2d38-4fd1-82a4-a125fd1de012","resolution":{"observed_at":"2026-08-01T10:25:17.232022Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-01T10:25:17.392856Z","title":null,"venue":null,"work_id":null,"year":2025},"citing_paper":{"arxiv_id":"2607.20279","last_updated":"2026-07-22T15:27:25Z","snapshot_observed_at":"2026-08-04T23:50:45.227058Z","submitted_at":"2026-07-22T15:27:25Z","title":"Random walks in Dirichlet random environment in dimension $d+1$","version":1},"reference_index":54,"source":"pdf_text","source_observed_at":"2026-08-01T10:25:17.392856Z"},"links":{"citing_paper":"/paper/2607.20279"},"observation_digest":"sha256:9633ff2f654fb0189afc614a1d1be7b4f3896773d2039e83d7862afa3f22a952","observation_id":"7aaa79fa-4ba3-43f1-b46b-cf622efcb131","resolution":{"observed_at":"2026-08-01T10:25:17.392856Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2405.04335","last_updated":"2025-01-08T12:23:21Z","snapshot_observed_at":"2026-08-08T16:50:13.162948Z","submitted_at":"2024-05-07T14:04:32Z","title":"The tail distribution of the partition function for directed polymer in the weak disorder phase","version":3},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2405.04335","snapshot_observed_at":"2026-08-01T10:25:17.530677Z","title":"Junk and H","venue":null,"work_id":null,"year":2024},"citing_paper":{"arxiv_id":"2607.20279","last_updated":"2026-07-22T15:27:25Z","snapshot_observed_at":"2026-08-04T23:50:45.227058Z","submitted_at":"2026-07-22T15:27:25Z","title":"Random walks in Dirichlet random environment in dimension $d+1$","version":1},"reference_index":55,"source":"pdf_text","source_observed_at":"2026-08-01T10:25:17.530677Z"},"links":{"cited_paper":"/paper/2405.04335","citing_paper":"/paper/2607.20279"},"observation_digest":"sha256:460c27ff7d54b2678c2eec69679cfc3fc11fc2e1f5f1ae09d24b02bf8f717948","observation_id":"161eefdb-3179-4812-94c3-313e160233c9","resolution":{"observed_at":"2026-08-01T10:25:17.530677Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-01T10:25:17.696289Z","title":"Meerson, P","venue":null,"work_id":null,"year":2018},"citing_paper":{"arxiv_id":"2607.20279","last_updated":"2026-07-22T15:27:25Z","snapshot_observed_at":"2026-08-04T23:50:45.227058Z","submitted_at":"2026-07-22T15:27:25Z","title":"Random walks in Dirichlet random environment in dimension $d+1$","version":1},"reference_index":56,"source":"pdf_text","source_observed_at":"2026-08-01T10:25:17.696289Z"},"links":{"citing_paper":"/paper/2607.20279"},"observation_digest":"sha256:83497d9ef1488881a1c06dc0601cf428e10bde128108f84890d4fda5b4b72b4d","observation_id":"8442ce10-d892-46ef-ae6d-ca7ff56ef033","resolution":{"observed_at":"2026-08-01T10:25:17.696289Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2505.13382","last_updated":"2025-05-19T17:25:15Z","snapshot_observed_at":"2026-08-07T15:43:01.306565Z","submitted_at":"2025-05-19T17:25:15Z","title":"The localization transition for the directed polymer in a random environment is smooth","version":1},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2505.13382","snapshot_observed_at":"2026-08-01T10:25:17.794478Z","title":"Lacoin, arXiv preprint arXiv:2505.13382 (2025)","venue":null,"work_id":null,"year":2025},"citing_paper":{"arxiv_id":"2607.20279","last_updated":"2026-07-22T15:27:25Z","snapshot_observed_at":"2026-08-04T23:50:45.227058Z","submitted_at":"2026-07-22T15:27:25Z","title":"Random walks in Dirichlet random environment in dimension $d+1$","version":1},"reference_index":57,"source":"pdf_text","source_observed_at":"2026-08-01T10:25:17.794478Z"},"links":{"cited_paper":"/paper/2505.13382","citing_paper":"/paper/2607.20279"},"observation_digest":"sha256:b6fd5e3ebd18e708a2dd7a603d62da45b91d08f59266be71d54ce2dfcc837117","observation_id":"56a83083-0dd1-467a-9d73-2cba19d0800e","resolution":{"observed_at":"2026-08-01T10:25:17.794478Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-01T10:25:17.981668Z","title":"Halpin-Healy, Physical Review E—Statistical, Nonlinear, and Soft Matter Physics88, 042118 (2013)","venue":null,"work_id":null,"year":2013},"citing_paper":{"arxiv_id":"2607.20279","last_updated":"2026-07-22T15:27:25Z","snapshot_observed_at":"2026-08-04T23:50:45.227058Z","submitted_at":"2026-07-22T15:27:25Z","title":"Random walks in Dirichlet random environment in dimension $d+1$","version":1},"reference_index":58,"source":"pdf_text","source_observed_at":"2026-08-01T10:25:17.981668Z"},"links":{"citing_paper":"/paper/2607.20279"},"observation_digest":"sha256:223a29d450faa21290867727a85fdd457876a372cdc7a7ab3eb0f19e753e8b83","observation_id":"17f1296f-428d-4963-9296-544bdf76a17f","resolution":{"observed_at":"2026-08-01T10:25:17.981668Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-01T10:25:18.074680Z","title":"Friedberg and Y.-K","venue":null,"work_id":null,"year":1994},"citing_paper":{"arxiv_id":"2607.20279","last_updated":"2026-07-22T15:27:25Z","snapshot_observed_at":"2026-08-04T23:50:45.227058Z","submitted_at":"2026-07-22T15:27:25Z","title":"Random walks in Dirichlet random environment in dimension $d+1$","version":1},"reference_index":59,"source":"pdf_text","source_observed_at":"2026-08-01T10:25:18.074680Z"},"links":{"citing_paper":"/paper/2607.20279"},"observation_digest":"sha256:e7685467ba9706228e136bbe2523c86880cc1032ed2c0b3e42e78374611b2371","observation_id":"e3ddc647-af00-4be3-9943-5c4ac3adc4d8","resolution":{"observed_at":"2026-08-01T10:25:18.074680Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-01T10:25:18.166118Z","title":null,"venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2607.20279","last_updated":"2026-07-22T15:27:25Z","snapshot_observed_at":"2026-08-04T23:50:45.227058Z","submitted_at":"2026-07-22T15:27:25Z","title":"Random walks in Dirichlet random environment in dimension $d+1$","version":1},"reference_index":60,"source":"pdf_text","source_observed_at":"2026-08-01T10:25:18.166118Z"},"links":{"citing_paper":"/paper/2607.20279"},"observation_digest":"sha256:c6c4878d85886b81990355cb04e70e4ba5a33f873ba8c3d2eeaa032007378274","observation_id":"5b07f148-bf6e-49be-a90c-1edff01396ed","resolution":{"observed_at":"2026-08-01T10:25:18.166118Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":"10.57782/g0hpxh","metadata_source":"openalex","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-05T02:28:24.338817Z","title":null,"venue":"Data Repository University Oldenburg","work_id":"53a578ef-d2a9-4e22-8629-54af01126c19","year":2026},"citing_paper":{"arxiv_id":"2607.20279","last_updated":"2026-07-22T15:27:25Z","snapshot_observed_at":"2026-08-04T23:50:45.227058Z","submitted_at":"2026-07-22T15:27:25Z","title":"Random walks in Dirichlet random environment in dimension $d+1$","version":1},"reference_index":61,"source":"pdf_text","source_observed_at":"2026-08-01T10:25:18.261662Z"},"links":{"citing_paper":"/paper/2607.20279"},"observation_digest":"sha256:529207eef969d06f431684eb6b4375e89742a09d46c22f72cf6d1af8dd39a4a9","observation_id":"6c5fb2d8-f6d6-4a2e-8732-c8aa36b5f0b7","resolution":{"observed_at":"2026-08-01T10:28:43.945384Z","resolver_source":"doi","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-09T06:31:02.800959+00:00","source":"crossref"},{"observed_at":"2026-08-09T06:30:57.326959+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-01T10:25:18.352309Z","title":"Erdos and S","venue":null,"work_id":null,"year":1960},"citing_paper":{"arxiv_id":"2607.20279","last_updated":"2026-07-22T15:27:25Z","snapshot_observed_at":"2026-08-04T23:50:45.227058Z","submitted_at":"2026-07-22T15:27:25Z","title":"Random walks in Dirichlet random environment in dimension $d+1$","version":1},"reference_index":62,"source":"pdf_text","source_observed_at":"2026-08-01T10:25:18.352309Z"},"links":{"citing_paper":"/paper/2607.20279"},"observation_digest":"sha256:44a0ffae8616525ac2967b53da07ca61280ee6ad0595a7e5dcb3f5c34f6a03aa","observation_id":"412a8dd1-f62b-4e1d-abbb-bf1477e772fb","resolution":{"observed_at":"2026-08-01T10:25:18.352309Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-01T10:25:18.408685Z","title":"Appendix A: Sample to sample variance of the thermal average In this section, we explain how to obtain the estimate (47) for the sample to sample variance of the thermal average","venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2607.20279","last_updated":"2026-07-22T15:27:25Z","snapshot_observed_at":"2026-08-04T23:50:45.227058Z","submitted_at":"2026-07-22T15:27:25Z","title":"Random walks in Dirichlet random environment in dimension $d+1$","version":1},"reference_index":63,"source":"pdf_text","source_observed_at":"2026-08-01T10:25:18.408685Z"},"links":{"citing_paper":"/paper/2607.20279"},"observation_digest":"sha256:af3fb63c86f035fb3cc2fd61fa9e86ae1c09260557a8d14a8de6355c0eedcb1a","observation_id":"1372eed8-5e31-4a1f-a564-fbd96a585145","resolution":{"observed_at":"2026-08-01T10:25:18.408685Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-01T10:25:18.469225Z","title":"Consider two random walksX 1(t),X 2(t) in the same environment","venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2607.20279","last_updated":"2026-07-22T15:27:25Z","snapshot_observed_at":"2026-08-04T23:50:45.227058Z","submitted_at":"2026-07-22T15:27:25Z","title":"Random walks in Dirichlet random environment in dimension $d+1$","version":1},"reference_index":64,"source":"pdf_text","source_observed_at":"2026-08-01T10:25:18.469225Z"},"links":{"citing_paper":"/paper/2607.20279"},"observation_digest":"sha256:9f86347c9be8288cd69e4dc03979dcbddc7541acc5735b8ddb61c6ee5c952b4b","observation_id":"095803cc-6cd5-4027-92c7-31d708db19af","resolution":{"observed_at":"2026-08-01T10:25:18.469225Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-01T10:25:18.558175Z","title":null,"venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2607.20279","last_updated":"2026-07-22T15:27:25Z","snapshot_observed_at":"2026-08-04T23:50:45.227058Z","submitted_at":"2026-07-22T15:27:25Z","title":"Random walks in Dirichlet random environment in dimension $d+1$","version":1},"reference_index":65,"source":"pdf_text","source_observed_at":"2026-08-01T10:25:18.558175Z"},"links":{"citing_paper":"/paper/2607.20279"},"observation_digest":"sha256:97490e5ed27d994d9707b498d2a4ebbd159b5d1587f3decc5d2cd8d1f3a58173","observation_id":"c6cba24b-b426-47cc-8447-a0fe61a8f7e4","resolution":{"observed_at":"2026-08-01T10:25:18.558175Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-01T10:25:18.645337Z","title":null,"venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2607.20279","last_updated":"2026-07-22T15:27:25Z","snapshot_observed_at":"2026-08-04T23:50:45.227058Z","submitted_at":"2026-07-22T15:27:25Z","title":"Random walks in Dirichlet random environment in dimension $d+1$","version":1},"reference_index":66,"source":"pdf_text","source_observed_at":"2026-08-01T10:25:18.645337Z"},"links":{"citing_paper":"/paper/2607.20279"},"observation_digest":"sha256:0d369f6ba1160a66ad4a22cf9eb5f4e3b6bd9c8ca30c0c0d64c07a5ee366cfc0","observation_id":"b3fefd62-b69c-43c9-a246-0e419fc41c81","resolution":{"observed_at":"2026-08-01T10:25:18.645337Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-01T10:25:18.738888Z","title":"In order to arrive at the pointvts 1, the walk must makessteps towardss 1 andt−ssteps in other directions, withss 1·s 1 +(t−s)s 1·s 2 =vts 1·s 1","venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2607.20279","last_updated":"2026-07-22T15:27:25Z","snapshot_observed_at":"2026-08-04T23:50:45.227058Z","submitted_at":"2026-07-22T15:27:25Z","title":"Random walks in Dirichlet random environment in dimension $d+1$","version":1},"reference_index":67,"source":"pdf_text","source_observed_at":"2026-08-01T10:25:18.738888Z"},"links":{"citing_paper":"/paper/2607.20279"},"observation_digest":"sha256:55308b687fc7889b6b4102c16cb9061a88923d55cf77785738451c44568520f8","observation_id":"f541ad1b-3f77-49af-b6d4-26711b301bcc","resolution":{"observed_at":"2026-08-01T10:25:18.738888Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-01T10:25:18.826524Z","title":null,"venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2607.20279","last_updated":"2026-07-22T15:27:25Z","snapshot_observed_at":"2026-08-04T23:50:45.227058Z","submitted_at":"2026-07-22T15:27:25Z","title":"Random walks in Dirichlet random environment in dimension $d+1$","version":1},"reference_index":68,"source":"pdf_text","source_observed_at":"2026-08-01T10:25:18.826524Z"},"links":{"citing_paper":"/paper/2607.20279"},"observation_digest":"sha256:e39c47337d746b9e77efa06eb948eacca42f427d1f75b9c2769945e416c94e30","observation_id":"1f64e498-5fdd-4acb-a86c-dd7e261bf06a","resolution":{"observed_at":"2026-08-01T10:25:18.826524Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-01T10:25:18.913359Z","title":null,"venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2607.20279","last_updated":"2026-07-22T15:27:25Z","snapshot_observed_at":"2026-08-04T23:50:45.227058Z","submitted_at":"2026-07-22T15:27:25Z","title":"Random walks in Dirichlet random environment in dimension $d+1$","version":1},"reference_index":69,"source":"pdf_text","source_observed_at":"2026-08-01T10:25:18.913359Z"},"links":{"citing_paper":"/paper/2607.20279"},"observation_digest":"sha256:1661edeec72c5edea8523a1740f113d50f87ffd467f4642b5c64bdd1b1cde9bc","observation_id":"200c9c78-4387-4350-8883-a5a8ac53ec48","resolution":{"observed_at":"2026-08-01T10:25:18.913359Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-01T10:25:18.978284Z","title":"From [42] (see also [19, 20, 44] ) we expect that this limit distribution has a power law tail with exponentµ(v)>µ(v c) = 1 + 2/d, i.e.,µ(vc) = 5/3 ind= 3","venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2607.20279","last_updated":"2026-07-22T15:27:25Z","snapshot_observed_at":"2026-08-04T23:50:45.227058Z","submitted_at":"2026-07-22T15:27:25Z","title":"Random walks in Dirichlet random environment in dimension $d+1$","version":1},"reference_index":70,"source":"pdf_text","source_observed_at":"2026-08-01T10:25:18.978284Z"},"links":{"citing_paper":"/paper/2607.20279"},"observation_digest":"sha256:f2858d034ef36b322854689d7b9112496267658090929f705edb06e3f0fdc2df","observation_id":"9a4cfa6f-87a6-41a7-b580-77bda8c26d4e","resolution":{"observed_at":"2026-08-01T10:25:18.978284Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}}],"paper":{"arxiv_id":"2607.20279","last_updated":"2026-07-22T15:27:25Z","latest_version":1,"primary_category":"cond-mat.stat-mech","snapshot_observed_at":"2026-08-04T23:50:45.227058Z","submitted_at":"2026-07-22T15:27:25Z","title":"Random walks in Dirichlet random environment in dimension $d+1$"},"reference_resolution":{"displayed":70,"state_counts":{"malformed_identifier":0,"metadata_mismatch":0,"parse_uncertain":0,"unresolved":69,"verified_exact":1,"verified_fuzzy":0},"total_outbound_references":70},"refusal":"A citation records a reference. It does not transfer a finding from one paper to another.","schema":"pith.paper-citation-record.v1","standing_sources":[{"observed_at":"2026-08-09T06:31:02.800959+00:00","source":"crossref"},{"observed_at":"2026-08-09T06:30:57.326959+00:00","source":"retraction_watch"}],"thesis":"As of 9 August 2026, this Paper Citation Record lists 70 of 70 outbound references and 0 inbound Pith citation observations for arXiv:2607.20279."}