{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2017:RTAU3ITPOBTACSB5AE6PKSX567","short_pith_number":"pith:RTAU3ITP","schema_version":"1.0","canonical_sha256":"8cc14da26f706601483d013cf54afdf7e1d1cf19840b07aa0df38155ce137c43","source":{"kind":"arxiv","id":"1707.01588","version":2},"attestation_state":"computed","paper":{"title":"Random polymers on the complete graph","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Alejandro F. Ramirez, Francis Comets, Gregorio R. Moreno Flores","submitted_at":"2017-07-05T21:53:38Z","abstract_excerpt":"Consider directed polymers in a random environment on the complete graph of size $N$. This model can be formulated as a product of i.i.d. $N\\times N$ random matrices and its large time asymptotics is captured by Lyapunov exponents and the Furstenberg measure. We detail this correspondence, derive the long-time limit of the model and obtain a co-variant distribution for the polymer path.\n  Next, we observe that the model becomes exactly solvable when the disorder variables are located on edges of the complete graph and follow a totally asymmetric stable law of index $\\alpha \\in (0,1)$. Then, a "},"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":"1707.01588","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2017-07-05T21:53:38Z","cross_cats_sorted":[],"title_canon_sha256":"ee5b355662a11a6512b1a48745be11273b422808b8f7c2705d967a89661a7d23","abstract_canon_sha256":"c7c2f6a0b597ff378520d5e54388a36f666e8dc7c555e14aafd37d23b4cdb612"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:25:34.237614Z","signature_b64":"zIwz1LOi+nBSPQnsbu9XFxwJ7e26BD/7pO0KHgEnPRFuu11rc6FA7/zfFdkgQtX3X/Kosyp1lxR1szSASjYOAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"8cc14da26f706601483d013cf54afdf7e1d1cf19840b07aa0df38155ce137c43","last_reissued_at":"2026-05-18T00:25:34.236837Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:25:34.236837Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Random polymers on the complete graph","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Alejandro F. Ramirez, Francis Comets, Gregorio R. Moreno Flores","submitted_at":"2017-07-05T21:53:38Z","abstract_excerpt":"Consider directed polymers in a random environment on the complete graph of size $N$. This model can be formulated as a product of i.i.d. $N\\times N$ random matrices and its large time asymptotics is captured by Lyapunov exponents and the Furstenberg measure. We detail this correspondence, derive the long-time limit of the model and obtain a co-variant distribution for the polymer path.\n  Next, we observe that the model becomes exactly solvable when the disorder variables are located on edges of the complete graph and follow a totally asymmetric stable law of index $\\alpha \\in (0,1)$. Then, a "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1707.01588","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":"1707.01588","created_at":"2026-05-18T00:25:34.236953+00:00"},{"alias_kind":"arxiv_version","alias_value":"1707.01588v2","created_at":"2026-05-18T00:25:34.236953+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1707.01588","created_at":"2026-05-18T00:25:34.236953+00:00"},{"alias_kind":"pith_short_12","alias_value":"RTAU3ITPOBTA","created_at":"2026-05-18T12:31:39.905425+00:00"},{"alias_kind":"pith_short_16","alias_value":"RTAU3ITPOBTACSB5","created_at":"2026-05-18T12:31:39.905425+00:00"},{"alias_kind":"pith_short_8","alias_value":"RTAU3ITP","created_at":"2026-05-18T12:31:39.905425+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/RTAU3ITPOBTACSB5AE6PKSX567","json":"https://pith.science/pith/RTAU3ITPOBTACSB5AE6PKSX567.json","graph_json":"https://pith.science/api/pith-number/RTAU3ITPOBTACSB5AE6PKSX567/graph.json","events_json":"https://pith.science/api/pith-number/RTAU3ITPOBTACSB5AE6PKSX567/events.json","paper":"https://pith.science/paper/RTAU3ITP"},"agent_actions":{"view_html":"https://pith.science/pith/RTAU3ITPOBTACSB5AE6PKSX567","download_json":"https://pith.science/pith/RTAU3ITPOBTACSB5AE6PKSX567.json","view_paper":"https://pith.science/paper/RTAU3ITP","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1707.01588&json=true","fetch_graph":"https://pith.science/api/pith-number/RTAU3ITPOBTACSB5AE6PKSX567/graph.json","fetch_events":"https://pith.science/api/pith-number/RTAU3ITPOBTACSB5AE6PKSX567/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/RTAU3ITPOBTACSB5AE6PKSX567/action/timestamp_anchor","attest_storage":"https://pith.science/pith/RTAU3ITPOBTACSB5AE6PKSX567/action/storage_attestation","attest_author":"https://pith.science/pith/RTAU3ITPOBTACSB5AE6PKSX567/action/author_attestation","sign_citation":"https://pith.science/pith/RTAU3ITPOBTACSB5AE6PKSX567/action/citation_signature","submit_replication":"https://pith.science/pith/RTAU3ITPOBTACSB5AE6PKSX567/action/replication_record"}},"created_at":"2026-05-18T00:25:34.236953+00:00","updated_at":"2026-05-18T00:25:34.236953+00:00"}