{"paper":{"title":"Maximal distance travelled by N vicious walkers till their survival","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cond-mat.dis-nn","math-ph","math.MP","math.PR"],"primary_cat":"cond-mat.stat-mech","authors_text":"Anupam Kundu, Gregory Schehr, Satya N. Majumdar","submitted_at":"2014-02-17T11:26:00Z","abstract_excerpt":"We consider $N$ Brownian particles moving on a line starting from initial positions ${\\bf{u}}\\equiv \\{u_1,u_2,\\dots u_N\\}$ such that $0<u_1 < u_2 < \\cdots < u_N$. Their motion gets stopped at time $t_s$ when either two of them collide or when the particle closest to the origin hits the origin for the first time. For $N=2$, we study the probability distribution function $p_1(m|{\\bf{u}})$ and $p_2(m|{\\bf{u}})$ of the maximal distance travelled by the $1^{\\text{st}}$ and $2^{\\text{nd}}$ walker till $t_s$. For general $N$ particles with identical diffusion constants $D$, we show that the probabili"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1402.3964","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"}