{"paper":{"title":"Phase Transitions of the Moran Process and Algorithmic Consequences","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.DM","cs.SI","math.CO","q-bio.PE"],"primary_cat":"math.PR","authors_text":"David Richerby, John Lapinskas, Leslie Ann Goldberg","submitted_at":"2018-04-06T14:23:15Z","abstract_excerpt":"The Moran process is a random process that models the spread of genetic mutations through graphs. If the graph is connected, the process eventually reaches \"fixation\", where every vertex is a mutant, or \"extinction\", where no vertex is a mutant.\n  Our main result is an almost-tight bound on expected absorption time. For all epsilon > 0, we show that the expected absorption time on an n-vertex graph is o(n^(3+epsilon)). In fact, we show that it is at most n^3 * exp(O((log log n)^3)) and that there is a family of graphs where it is Omega(n^3). In the course of proving our main result, we also es"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1804.02293","kind":"arxiv","version":4},"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"}