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Mountford","submitted_at":"2016-02-17T17:16:52Z","abstract_excerpt":"We consider the Anderson polymer partition function $$ u(t):=\\mathbb{E}^X\\Bigl[e^{\\int_0^t \\mathrm{d}B^{X(s)}_s}\\Bigr]\\,, $$ where $\\{B^{x}_t\\,;\\, t\\geq0\\}_{x\\in\\mathbb{Z}^d}$ is a family of independent fractional Brownian motions all with Hurst parameter $H\\in(0,1)$, and $\\{X(t)\\}_{t\\in \\mathbb{R}^{\\geq 0}}$ is a continuous-time simple symmetric random walk on $\\mathbb{Z}^d$ with jump rate $\\kappa$ and started from the origin. $\\mathbb{E}^X$ is the expectation with respect to this random walk.\n  We prove that when $H\\leq 1/2$, the function $u(t)$ almost surely grows asymptotically like $e^{l "},"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":"1602.05491","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2016-02-17T17:16:52Z","cross_cats_sorted":[],"title_canon_sha256":"3b993b69b09426b9b3f7cef59f78ca204a4da8b37ec15251db4a37c4aaeec6c7","abstract_canon_sha256":"5a2efb0b097938e57ac3824c979c54580fcf039bc80a78fb91996bb4f4db8485"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:36:09.950637Z","signature_b64":"FVeBngDy7S6A9L7RnuYdaXfHQIghU4jop+W4n4cfA18slwKG20/oZbZXVevB9rW/FQqLj2ZL+E1hxSfGBvtGCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"f72abbb37f480b60e0edb8eb432dd1536c0f726b247f400f286f36eb1ef7aa8c","last_reissued_at":"2026-05-18T00:36:09.949949Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:36:09.949949Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Anderson polymer in a fractional Brownian environment: asymptotic behavior of the partition function","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Frederi G. Viens, Kamran Kalbasi, Thomas S. Mountford","submitted_at":"2016-02-17T17:16:52Z","abstract_excerpt":"We consider the Anderson polymer partition function $$ u(t):=\\mathbb{E}^X\\Bigl[e^{\\int_0^t \\mathrm{d}B^{X(s)}_s}\\Bigr]\\,, $$ where $\\{B^{x}_t\\,;\\, t\\geq0\\}_{x\\in\\mathbb{Z}^d}$ is a family of independent fractional Brownian motions all with Hurst parameter $H\\in(0,1)$, and $\\{X(t)\\}_{t\\in \\mathbb{R}^{\\geq 0}}$ is a continuous-time simple symmetric random walk on $\\mathbb{Z}^d$ with jump rate $\\kappa$ and started from the origin. $\\mathbb{E}^X$ is the expectation with respect to this random walk.\n  We prove that when $H\\leq 1/2$, the function $u(t)$ almost surely grows asymptotically like $e^{l "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1602.05491","kind":"arxiv","version":2},"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":"1602.05491","created_at":"2026-05-18T00:36:09.950062+00:00"},{"alias_kind":"arxiv_version","alias_value":"1602.05491v2","created_at":"2026-05-18T00:36:09.950062+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1602.05491","created_at":"2026-05-18T00:36:09.950062+00:00"},{"alias_kind":"pith_short_12","alias_value":"64VLXM37JAFW","created_at":"2026-05-18T12:30:01.593930+00:00"},{"alias_kind":"pith_short_16","alias_value":"64VLXM37JAFWBYHN","created_at":"2026-05-18T12:30:01.593930+00:00"},{"alias_kind":"pith_short_8","alias_value":"64VLXM37","created_at":"2026-05-18T12:30:01.593930+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/64VLXM37JAFWBYHNXDVUGLORKN","json":"https://pith.science/pith/64VLXM37JAFWBYHNXDVUGLORKN.json","graph_json":"https://pith.science/api/pith-number/64VLXM37JAFWBYHNXDVUGLORKN/graph.json","events_json":"https://pith.science/api/pith-number/64VLXM37JAFWBYHNXDVUGLORKN/events.json","paper":"https://pith.science/paper/64VLXM37"},"agent_actions":{"view_html":"https://pith.science/pith/64VLXM37JAFWBYHNXDVUGLORKN","download_json":"https://pith.science/pith/64VLXM37JAFWBYHNXDVUGLORKN.json","view_paper":"https://pith.science/paper/64VLXM37","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1602.05491&json=true","fetch_graph":"https://pith.science/api/pith-number/64VLXM37JAFWBYHNXDVUGLORKN/graph.json","fetch_events":"https://pith.science/api/pith-number/64VLXM37JAFWBYHNXDVUGLORKN/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/64VLXM37JAFWBYHNXDVUGLORKN/action/timestamp_anchor","attest_storage":"https://pith.science/pith/64VLXM37JAFWBYHNXDVUGLORKN/action/storage_attestation","attest_author":"https://pith.science/pith/64VLXM37JAFWBYHNXDVUGLORKN/action/author_attestation","sign_citation":"https://pith.science/pith/64VLXM37JAFWBYHNXDVUGLORKN/action/citation_signature","submit_replication":"https://pith.science/pith/64VLXM37JAFWBYHNXDVUGLORKN/action/replication_record"}},"created_at":"2026-05-18T00:36:09.950062+00:00","updated_at":"2026-05-18T00:36:09.950062+00:00"}