{"paper":{"title":"The replicator equation in stochastic spatial evolutionary games","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["q-bio.PE"],"primary_cat":"math.PR","authors_text":"Yu-Ting Chen","submitted_at":"2020-10-12T20:58:36Z","abstract_excerpt":"We study the multi-strategy stochastic evolutionary game with death-birth updating in expanding spatial populations of size $N\\to \\infty$. The model is a voter model perturbation. For typical populations, we require perturbation strengths satisfying $1/N\\ll w\\ll 1$. Under appropriate conditions on the space, the limiting density processes of strategy are proven to obey the replicator equation, and the normalized fluctuations converge to a Gaussian process with the Wright-Fisher covariance function in the limiting densities. As an application, we resolve in the positive a conjecture from the bi"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2010.06025","kind":"arxiv","version":3},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2010.06025/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"}