{"paper":{"title":"PDEs satisfied by extreme eigenvalues distributions of GUE and LUE","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.MP","math.PR"],"primary_cat":"math-ph","authors_text":"Estelle Basor, Lun Zhang, Yang Chen","submitted_at":"2011-02-02T11:06:19Z","abstract_excerpt":"In this paper we study, $\\textsf{Prob}(n,a,b),$ the probability that all the eigenvalues of finite $n$ unitary ensembles lie in the interval $(a,b)$. This is identical to the probability that the largest eigenvalue is less than $b$ and the smallest eigenvalue is greater than $a$. It is shown that a quantity allied to $\\textsf{Prob}(n,a,b)$, namely, $$ H_n(a,b):=\\left[\\frac{\\partial}{\\partial a}+\\frac{\\partial}{\\partial b}\\right]\\ln\\textsf{Prob}(n,a,b),$$ in the Gaussian Unitary Ensemble (GUE) and $$ H_n(a,b):=\\left[a\\frac{\\partial}{\\partial a}+b\\frac{\\partial}{\\partial b}\\right]\\ln \\textsf{Pro"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1102.0402","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"}