{"paper":{"title":"The speed of a random front for stochastic reaction-diffusion equations with strong noise","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Carl Mueller, Lenya Ryzhik, Leonid Mytnik","submitted_at":"2019-03-08T19:45:54Z","abstract_excerpt":"We study the asymptotic speed of a random front for solutions $u_t(x)$ to stochastic reaction-diffusion equations of the form \\[ \\partial_tu=\\farc{1}{2}\\partial_x^2u+f(u)+\\sigma\\sqrt{u(1-u)}\\dot{W}(t,x),~t\\ge 0,~x\\in\\Rm, \\] arising in population genetics. Here, $f$ is a continuous function with $f(0)=f(1)=0$, and such that~$|f(u)|\\le K|u(1-u)|^\\gamma$ with~$\\gamma\\ge 1/2$, and $\\dot{W}(t,x)$ is a space-time Gaussian white noise. We assume that the initial condition $u_0(x)$ satisfies $0\\le u_0(x)\\le 1$ for all $x\\in\\Rm$, $u_0(x)=1$ for~$x<L_0$ and $ u_0(x)=0$ for~$x>R_0$. We show that when $\\s"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1903.03645","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"}