{"paper":{"title":"Branching Brownian motion with decay of mass and 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":"Julien Berestycki, Louigi Addario-Berry, Sarah Penington","submitted_at":"2017-12-21T17:26:35Z","abstract_excerpt":"In this work we study a non-local version of the Fisher-KPP equation, \\begin{equation*} \\begin{cases} \\frac{\\partial u}{\\partial t}=\\tfrac{1}{2}\\Delta u +u (1- \\phi \\ast u), \\quad t>0, \\quad x\\in \\mathbb{R}, u(0,x)=u_0(x), \\quad x\\in \\mathbb{R} \\end{cases} \\end{equation*} and its relation to $\\textit{branching Brownian motion with decay of mass}$ as introduced by Addario-Berry and Penington (2017), i.e. a particle system consisting of a standard branching Brownian motion (BBM) with a competitive interaction between nearby particles. Particles in the BBM with decay of mass have a position in $\\"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1712.08098","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"}