{"paper":{"title":"Edge Universality for Nonintersecting Brownian Bridges","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Jiaoyang Huang","submitted_at":"2020-11-03T14:57:24Z","abstract_excerpt":"In this paper we study fluctuations of extreme particles of nonintersecting Brownian bridges starting from $a_1\\leq a_2\\leq \\cdots \\leq a_n$ at time $t=0$ and ending at $b_1\\leq b_2\\leq \\cdots\\leq b_n$ at time $t=1$, where $\\mu_{A_n}=(1/n)\\sum_{i}\\delta_{a_i}, \\mu_{B_n}=(1/n)\\sum_i \\delta_{b_i}$ are discretization of probability measures $\\mu_A, \\mu_B$. Under regularity assumptions of $\\mu_A, \\mu_B$, we show as the number of particles $n$ goes to infinity, fluctuations of extreme particles at any time $0<t<1$, after proper rescaling, are asymptotically universal, converging to the Airy point p"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2011.01752","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2011.01752/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"}