{"paper":{"title":"Survival of near-critical branching Brownian motion","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Jason Schweinsberg, Julien Berestycki, Nathana\\\"el Berestycki","submitted_at":"2010-09-02T12:21:53Z","abstract_excerpt":"Consider a system of particles performing branching Brownian motion with negative drift $\\mu = \\sqrt{2 - \\epsilon}$ and killed upon hitting zero. Initially there is one particle at $x>0$. Kesten showed that the process survives with positive probability if and only if $\\epsilon>0$. Here we are interested in the asymptotics as $\\eps\\to 0$ of the survival probability $Q_\\mu(x)$. It is proved that if $L= \\pi/\\sqrt{\\epsilon}$ then for all $x \\in \\R$, $\\lim_{\\epsilon \\to 0} Q_\\mu(L+x) = \\theta(x) \\in (0,1)$ exists and is a travelling wave solution of the Fisher-KPP equation. Furthermore, we obtain "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1009.0406","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"}