{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:LOIYN3U5OA66HY7XHOWAYR5TJ6","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"d969b56bb32eefb1851213fce0b7f00a98d29a35f6bd9aa65f5a9f9d9e3194d9","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2012-07-27T08:13:43Z","title_canon_sha256":"06a2cdd67d05e0cbecc926f27399f9a9edbf55fd2e695ee4593a4523d5e79a5f"},"schema_version":"1.0","source":{"id":"1207.6483","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1207.6483","created_at":"2026-05-18T03:49:59Z"},{"alias_kind":"arxiv_version","alias_value":"1207.6483v1","created_at":"2026-05-18T03:49:59Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1207.6483","created_at":"2026-05-18T03:49:59Z"},{"alias_kind":"pith_short_12","alias_value":"LOIYN3U5OA66","created_at":"2026-05-18T12:27:14Z"},{"alias_kind":"pith_short_16","alias_value":"LOIYN3U5OA66HY7X","created_at":"2026-05-18T12:27:14Z"},{"alias_kind":"pith_short_8","alias_value":"LOIYN3U5","created_at":"2026-05-18T12:27:14Z"}],"graph_snapshots":[{"event_id":"sha256:566106dd60f0b08c0be3d5c659329d17a12e365dec9a50e50c808302680dd400","target":"graph","created_at":"2026-05-18T03:49:59Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"paper":{"abstract_excerpt":"Let $B_s$ be a $d$-dimensional Brownian motion and $\\omega(dx)$ be an independent Poisson field on $\\mathbb{R}^d$. The almost sure asymptotics for the logarithmic moment generating function [\\log\\math bb{E}_0\\exp\\biggl{\\pm\\theta\\int_0^t\\bar{V}(B_s) ds\\biggr}\\qquad (t\\to\\infty)] are investigated in connection with the renormalized Poisson potential of the form [\\bar{V}(x)=\\int_{\\mathbb{R}^d}{\\frac{1}{|y-x|^p}}[\\omega(dy)-dy],\\qquad x\\in\\mathbb{R}^d.] The investigation is motivated by some practical problems arising from the models of Brownian motion in random media and from the parabolic Anders","authors_text":"Xia Chen","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2012-07-27T08:13:43Z","title":"Quenched asymptotics for Brownian motion of renormalized Poisson potential and for the related parabolic Anderson models"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1207.6483","kind":"arxiv","version":1},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:ad7025e72a305e89168d09083e385354ec3d447f6fcf16bcc9aa000c6a1f9d9a","target":"record","created_at":"2026-05-18T03:49:59Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"d969b56bb32eefb1851213fce0b7f00a98d29a35f6bd9aa65f5a9f9d9e3194d9","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2012-07-27T08:13:43Z","title_canon_sha256":"06a2cdd67d05e0cbecc926f27399f9a9edbf55fd2e695ee4593a4523d5e79a5f"},"schema_version":"1.0","source":{"id":"1207.6483","kind":"arxiv","version":1}},"canonical_sha256":"5b9186ee9d703de3e3f73bac0c47b34f967085e0feffa43a7ca75c91823dd2dc","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"5b9186ee9d703de3e3f73bac0c47b34f967085e0feffa43a7ca75c91823dd2dc","first_computed_at":"2026-05-18T03:49:59.200606Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:49:59.200606Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"HkYO2kXZAdTcvkvZ3y/BwNQdcYisKo2tGyJMQS1CLrJH9+apfr9NHSQFbh+wzGoHuzRhg7337hX3ZR9zjsIPDA==","signature_status":"signed_v1","signed_at":"2026-05-18T03:49:59.201379Z","signed_message":"canonical_sha256_bytes"},"source_id":"1207.6483","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:ad7025e72a305e89168d09083e385354ec3d447f6fcf16bcc9aa000c6a1f9d9a","sha256:566106dd60f0b08c0be3d5c659329d17a12e365dec9a50e50c808302680dd400"],"state_sha256":"fd8648e9cc394df75bed2304e872554a7ad41cbefb7e7ceb3824db99bfe1bea4"}