{"paper":{"title":"The spreading speed of solutions of the non-local Fisher-KPP equation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AP"],"primary_cat":"math.PR","authors_text":"Sarah Penington","submitted_at":"2017-08-26T13:02:51Z","abstract_excerpt":"We consider the Fisher-KPP equation with a non-local interaction term. Hamel and Ryzhik showed that in solutions of this equation, the front location at a large time $t$ is $\\sqrt 2 t +o(t)$. We study the asymptotics of the second order term in the front location. If the interaction kernel $\\phi(x)$ decays sufficiently fast as $x\\rightarrow \\infty$ then this term is given by $-\\frac{3}{2\\sqrt 2 }\\log t +o(\\log t)$, which is the same correction as found by Bramson for the local Fisher-KPP equation. However, if $\\phi$ has a heavier tail then the second order term is $-t^{\\beta +o(1)}$, where $\\b"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1708.07965","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"}