{"paper":{"title":"Refined long time asymptotics for Fisher-KPP fronts","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"James Nolen, Jean-Michel Roquejoffre, Lenya Ryzhik","submitted_at":"2016-07-29T13:34:44Z","abstract_excerpt":"We study the one-dimensional Fisher-KPP equation, with an initial condition $u_0(x)$ that coincides with the step function except on a compact set. A well-known result of M. Bramson states that, as $t\\to+\\infty$, the solution converges to a traveling wave located at the position $X(t)=2t-(3/2)\\log t+x_0+o(1)$, with the shift $x_0$ that depends on $u_0$. U. Ebert and W. Van Saarloos have formally derived a correction to the Bramson shift, arguing that $X(t)=2t-(3/2)\\log t+x_0-3\\sqrt{\\pi}/\\sqrt{t}+O(1/t)$. Here, we prove that this result does hold, with an error term of the size $O(1/t^{1-\\gamma"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1607.08802","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"}