{"paper":{"title":"Extremes of N vicious walkers for large N: application to the directed polymer and KPZ interfaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cond-mat.dis-nn","cond-mat.stat-mech","math.MP","math.PR"],"primary_cat":"math-ph","authors_text":"Gregory Schehr","submitted_at":"2012-03-07T23:27:36Z","abstract_excerpt":"We compute the joint probability density function (jpdf) P_N(M, \\tau_M) of the maximum M and its position \\tau_M for N non-intersecting Brownian excursions, on the unit time interval, in the large N limit. For N \\to \\infty, this jpdf is peaked around M = \\sqrt{2N} and \\tau_M = 1/2, while the typical fluctuations behave for large N like M - \\sqrt{2N} \\propto s N^{-1/6} and \\tau_M - 1/2 \\propto w N^{-1/3} where s and w are correlated random variables. One obtains an explicit expression of the limiting jpdf P(s,w) in terms of the Tracy-Widom distribution for the Gaussian Orthogonal Ensemble (GOE)"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1203.1658","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"}