{"paper":{"title":"Local universality in biorthogonal Laguerre ensembles","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CA","math.MP","math.PR"],"primary_cat":"math-ph","authors_text":"Lun Zhang","submitted_at":"2015-02-11T00:37:14Z","abstract_excerpt":"We consider $n$ particles $0\\leq x_1<x_2< \\cdots < x_n < +\\infty$, distributed according to a probability measure of the form $$ \\frac{1}{Z_n}\\prod_{1\\leq i <j \\leq n}(x_j-x_i)\\prod_{1\\leq i <j \\leq n}(x_j^{\\theta}-x_i^{\\theta})\\prod_{j=1}^nx_j^\\alpha e^{-x_j}\\ud x_j, ~~ \\alpha>-1,~~ \\theta>0, $$ where $Z_n$ is the normalization constant. This distribution arises in the context of modeling disordered conductors in the metallic regime, and can also be realized as the distribution for squared singular values of certain triangular random matrices. We give a double contour integral formula for the"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1502.03160","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"}