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The mutation probability per locus is $q$. The replication rate is $\\sigma>1$ for the master sequence and $1$ for the other sequences. We study the equilibrium distribution of the process in the regime where $\\ell\\to+\\infty$, $m\\to+\\infty$, $q\\to0$, $\\ell q\\to a\\in\\,]0,+\\infty[$, $\\frac{m}{\\ell}\\to\\alpha\\in [0,+\\infty]$. We obtain an equation"},"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":"1207.0673","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2012-07-03T13:39:41Z","cross_cats_sorted":["q-bio.PE"],"title_canon_sha256":"d2f3806224c0abc0a5e3cd55d51c29a6c6ad1279a5cb87edf5ba5fef13f9d6a4","abstract_canon_sha256":"9446cbb405a5d95151c1e81d0eb22ffdd4c592f0103dcb87cd8a925a602ee1dc"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:09:28.488879Z","signature_b64":"Tc1qf/11zzZvy9L4tCk/XwLv2jtzlfX6EwtQA27KkmrhPMnsVms0d4fOZp8ogngShgNSyinECHCv5h/em8axDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"861c753de648d8a4d36b5f2d980ce27973a2b2da40660c3d637833c0cdfd07c5","last_reissued_at":"2026-05-18T01:09:28.488479Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:09:28.488479Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Critical population and error threshold on the sharp peak landscape for the Wright-Fisher model","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["q-bio.PE"],"primary_cat":"math.PR","authors_text":"Rapha\\\"el Cerf","submitted_at":"2012-07-03T13:39:41Z","abstract_excerpt":"We pursue the task of developing a finite population counterpart to Eigen's model. We consider the classical Wright-Fisher model describing the evolution of a population of size $m$ of chromosomes of length $\\ell$ over an alphabet of cardinality $\\kappa$. The mutation probability per locus is $q$. The replication rate is $\\sigma>1$ for the master sequence and $1$ for the other sequences. We study the equilibrium distribution of the process in the regime where $\\ell\\to+\\infty$, $m\\to+\\infty$, $q\\to0$, $\\ell q\\to a\\in\\,]0,+\\infty[$, $\\frac{m}{\\ell}\\to\\alpha\\in [0,+\\infty]$. 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