{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2015:MXBEUAFG3M6MWFMDQENDQYP7Y5","short_pith_number":"pith:MXBEUAFG","schema_version":"1.0","canonical_sha256":"65c24a00a6db3ccb1583811a3861ffc744161173529ce1e1cb672f52ac72ff83","source":{"kind":"arxiv","id":"1501.05929","version":1},"attestation_state":"computed","paper":{"title":"Random walks and isoperimetric profiles under moment conditions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.GR"],"primary_cat":"math.PR","authors_text":"Laurent Saloff-Coste, Tianyi Zheng","submitted_at":"2015-01-23T19:55:51Z","abstract_excerpt":"Let $G$ be a finitely generated group equipped with a finite symmetric generating set and the associated word length function $|\\cdot |$. We study the behavior of the probability of return for random walks driven by symmetric measures $\\mu$ that are such that $\\sum \\rho(|x|)\\mu(x)<\\infty$ for increasing regularly varying or slowly varying functions $\\rho$, for instance, $s\\mapsto (1+s)^\\alpha$, $\\alpha\\in (0,2]$, or $s\\mapsto (1+\\log (1+s))^\\epsilon$, $\\epsilon>0$. For this purpose we develop new relations between the isoperimetric profiles associated with different symmetric probability measu"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1501.05929","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2015-01-23T19:55:51Z","cross_cats_sorted":["math.GR"],"title_canon_sha256":"1eac293f9b9b9b84617e29c4750f1c5fa02eff6173fddc874b70c99b18299d75","abstract_canon_sha256":"31c2f512bbe5ad7e7ddc1ad4a0d1d29bb6e99960c01fe7ebf9d3f22cc3a63d53"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:28:48.727296Z","signature_b64":"TgJL+uMhePH7gvkjrwUYcRkAi+FeyywqbZFcpIWjugPdJ4BZ2KJmt52BSBeJhW2oEFSR1lcX338V+y3jMt6ZBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"65c24a00a6db3ccb1583811a3861ffc744161173529ce1e1cb672f52ac72ff83","last_reissued_at":"2026-05-18T02:28:48.726963Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:28:48.726963Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Random walks and isoperimetric profiles under moment conditions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.GR"],"primary_cat":"math.PR","authors_text":"Laurent Saloff-Coste, Tianyi Zheng","submitted_at":"2015-01-23T19:55:51Z","abstract_excerpt":"Let $G$ be a finitely generated group equipped with a finite symmetric generating set and the associated word length function $|\\cdot |$. We study the behavior of the probability of return for random walks driven by symmetric measures $\\mu$ that are such that $\\sum \\rho(|x|)\\mu(x)<\\infty$ for increasing regularly varying or slowly varying functions $\\rho$, for instance, $s\\mapsto (1+s)^\\alpha$, $\\alpha\\in (0,2]$, or $s\\mapsto (1+\\log (1+s))^\\epsilon$, $\\epsilon>0$. For this purpose we develop new relations between the isoperimetric profiles associated with different symmetric probability measu"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1501.05929","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"aliases":[{"alias_kind":"arxiv","alias_value":"1501.05929","created_at":"2026-05-18T02:28:48.727018+00:00"},{"alias_kind":"arxiv_version","alias_value":"1501.05929v1","created_at":"2026-05-18T02:28:48.727018+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1501.05929","created_at":"2026-05-18T02:28:48.727018+00:00"},{"alias_kind":"pith_short_12","alias_value":"MXBEUAFG3M6M","created_at":"2026-05-18T12:29:32.376354+00:00"},{"alias_kind":"pith_short_16","alias_value":"MXBEUAFG3M6MWFMD","created_at":"2026-05-18T12:29:32.376354+00:00"},{"alias_kind":"pith_short_8","alias_value":"MXBEUAFG","created_at":"2026-05-18T12:29:32.376354+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/MXBEUAFG3M6MWFMDQENDQYP7Y5","json":"https://pith.science/pith/MXBEUAFG3M6MWFMDQENDQYP7Y5.json","graph_json":"https://pith.science/api/pith-number/MXBEUAFG3M6MWFMDQENDQYP7Y5/graph.json","events_json":"https://pith.science/api/pith-number/MXBEUAFG3M6MWFMDQENDQYP7Y5/events.json","paper":"https://pith.science/paper/MXBEUAFG"},"agent_actions":{"view_html":"https://pith.science/pith/MXBEUAFG3M6MWFMDQENDQYP7Y5","download_json":"https://pith.science/pith/MXBEUAFG3M6MWFMDQENDQYP7Y5.json","view_paper":"https://pith.science/paper/MXBEUAFG","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1501.05929&json=true","fetch_graph":"https://pith.science/api/pith-number/MXBEUAFG3M6MWFMDQENDQYP7Y5/graph.json","fetch_events":"https://pith.science/api/pith-number/MXBEUAFG3M6MWFMDQENDQYP7Y5/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/MXBEUAFG3M6MWFMDQENDQYP7Y5/action/timestamp_anchor","attest_storage":"https://pith.science/pith/MXBEUAFG3M6MWFMDQENDQYP7Y5/action/storage_attestation","attest_author":"https://pith.science/pith/MXBEUAFG3M6MWFMDQENDQYP7Y5/action/author_attestation","sign_citation":"https://pith.science/pith/MXBEUAFG3M6MWFMDQENDQYP7Y5/action/citation_signature","submit_replication":"https://pith.science/pith/MXBEUAFG3M6MWFMDQENDQYP7Y5/action/replication_record"}},"created_at":"2026-05-18T02:28:48.727018+00:00","updated_at":"2026-05-18T02:28:48.727018+00:00"}