{"paper":{"title":"Universality of local statistics for noncolliding random walks","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.CO","math.MP","math.RT"],"primary_cat":"math.PR","authors_text":"Leonid Petrov, Vadim Gorin","submitted_at":"2016-08-10T18:07:41Z","abstract_excerpt":"We consider the $N$-particle noncolliding Bernoulli random walk --- a discrete time Markov process in $\\mathbb{Z}^{N}$ obtained from a collection of $N$ independent simple random walks with steps $\\in\\{0,1\\}$ by conditioning that they never collide. We study the asymptotic behavior of local statistics of this process started from an arbitrary initial configuration on short times $T\\ll N$ as $N\\to+\\infty$. We show that if the particle density of the initial configuration is bounded away from $0$ and $1$ down to scales $\\mathsf{D}\\ll T$ in a neighborhood of size $\\mathsf{Q}\\gg T$ of some locatio"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1608.03243","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"}