{"paper":{"title":"Critical edge behavior in the perturbed Laguerre ensemble and the Painleve V transcendent","license":"http://creativecommons.org/licenses/by-nc-sa/4.0/","headline":"","cross_cats":["math.MP","nlin.SI"],"primary_cat":"math-ph","authors_text":"Engui Fan, Min Chen, Yang Chen","submitted_at":"2017-11-13T00:27:37Z","abstract_excerpt":"In this paper, we consider the perturbed Laguerre unitary ensemble described by the weight function of $$w(x,t)=(x+t)^{\\lambda}x^{\\alpha}e^{-x}$$ with $ x\\geq 0,\\ t>0,\\ \\alpha>0,\\ \\alpha+\\lambda+1 > 0.$ The Deift-Zhou nonlinear steepest descent approach is used to analyze the limit of the eigenvalue correlation kernel. It was found that under the double scaling $s=4nt,$ $n\\to \\infty,$ $t\\to 0 $ such that $s$ is positive and finite, at the hard edge, the limiting kernel can be described by the $\\varphi$-function related to a third-order nonlinear differential equation, which is equivalent to a "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1711.04383","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"}