{"paper":{"title":"Evolutionary Games on the Torus with Weak Selection","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"J.T. Cox, Rick Durrett","submitted_at":"2015-11-15T15:30:07Z","abstract_excerpt":"We study evolutionary games on the torus with $N$ points in dimensions $d\\ge 3$. The matrices have the form $\\bar G = {\\bf 1} + w G$, where ${\\bf 1}$ is a matrix that consists of all 1's, and $w$ is small. As in Cox Durrett and Perkins \\cite{CDP} we rescale time and space and take a limit as $N\\to\\infty$ and $w\\to 0$. If (i) $w \\gg N^{-2/d}$ then the limit is a PDE on ${\\bf R}^d$. If (ii) $N^{-2/d} \\gg w \\gg N^{-1}$, then the limit is an ODE. If (iii) $w \\ll N^{-1}$ then the effect of selection vanishes in the limit. In regime (ii) if we introduce a mutation $\\mu$ so that $\\mu /w \\to \\infty$ s"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1511.04713","kind":"arxiv","version":1},"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"}