{"paper":{"title":"Asymptotic Behaviour of an Infinitely-Many-Alleles Diffusion with Symmetric Overdonminance","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Youzhou Zhou","submitted_at":"2013-03-27T11:51:41Z","abstract_excerpt":"This paper considers the limiting distribution of $\\pi_{\\lambda,\\theta}$, the stationary distribution of the infinitely-many-alleles diffusion with symmetric overdominance \\cite{MR1626158}. In \\cite{MR2519357} the large deviation principle for $\\pi_{\\lambda,\\theta}$ indicates that there are countably many phase transitions for the limiting distribution of $\\pi_{\\lambda,\\theta}$, and the critical points are $\\lambda=k(k+1), k\\geq1$. The asymptotic behaviours at those critical points, however, are unclear. This article provides a definite description of the critical cases."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1303.6797","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"}