{"paper":{"title":"Branching Brownian motion with absorption and the all-time minimum of branching Brownian motion with drift","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"\\'Eric Brunet, Julien Berestycki, Piotr Mi{\\l}o\\'s, Simon C. Harris","submitted_at":"2015-06-03T23:12:29Z","abstract_excerpt":"We study a dyadic branching Brownian motion on the real line with absorption at 0, drift $\\mu \\in \\mathbb{R}$ and started from a single particle at position $x>0.$ When $\\mu$ is large enough so that the process has a positive probability of survival, we consider $K(t),$ the number of individuals absorbed at 0 by time $t$ and for $s\\ge 0$ the functions $\\omega_s(x):= \\mathbb{E}^x[s^{K(\\infty)}].$ We show that $\\omega_s<\\infty$ if and only of $s\\in[0,s_0]$ for some $s_0>1$ and we study the properties of these functions. Furthermore, for $s=0, \\omega(x) := \\omega_0(x) =\\mathbb{P}^x(K(\\infty)=0)$ "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1506.01429","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"}