{"paper":{"title":"Spatial Extent of Branching Brownian Motion","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP","math.PR"],"primary_cat":"cond-mat.stat-mech","authors_text":"Gregory Schehr, Kabir Ramola, Satya N. Majumdar","submitted_at":"2015-01-30T08:20:38Z","abstract_excerpt":"We study the one dimensional branching Brownian motion starting at the origin and investigate the correlation between the rightmost ($X_{\\max}\\geq 0$) and leftmost ($X_{\\min} \\leq 0$) visited sites up to time $t$. At each time step the existing particles in the system either diffuse (with diffusion constant $D$), die (with rate $a$) or split into two particles (with rate $b$). We focus on the regime $b \\leq a$ where these two extreme values $X_{\\max}$ and $X_{\\min}$ are strongly correlated. We show that at large time $t$, the joint probability distribution function (PDF) of the two extreme poi"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1501.07693","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"}