{"paper":{"title":"Singular linear statistics of the Laguerre Unitary Ensemble and Painlev\\'e III (${\\rm P_{III}}$): Double scaling analysis","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CA","authors_text":"Min Chen, Yang Chen","submitted_at":"2014-11-29T12:49:04Z","abstract_excerpt":"We continue with the study of the Hankel determinant, $$ D_{n}(t,\\alpha):=\\det\\left(\\int_{0}^{\\infty}x^{j+k}w(x;t,\\alpha)dx\\right)_{j,k=0 }^{n-1}, $$ generated by singularly perturbed Laguerre weight, $$ w(x;t,\\alpha):=x^{\\alpha}{\\rm e}^{-x}\\:{\\rm e}^{-t/x}, \\quad 0\\leq x<\\infty,\\;\\;\\;\\alpha>0,\\;\\;\\;\\;t>0, $$ obtained through a deformation of the Laguerre weight function, $$ w(x;0,\\alpha):=x^{\\alpha}{\\rm e}^{-x},\\quad 0\\leq x<\\infty,\\;\\; \\alpha>0, $$ via the multiplicative factor ${\\rm e}^{-t/x}$. \\\\ An earlier investigation was made on the finite $n$ aspect of the problem, this has appeared i"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1412.0102","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"}