{"paper":{"title":"Painlev\\'e III asymptotics of Hankel determinants for a singularly perturbed Laguerre weight","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CA","authors_text":"Dan Dai, Shuai-Xia Xu, Yu-Qiu Zhao","submitted_at":"2014-07-28T06:47:07Z","abstract_excerpt":"In this paper, we consider the Hankel determinants associated with the singularly perturbed Laguerre weight $w(x)=x^\\alpha e^{-x-t/x}$, $x\\in (0, \\infty)$, $t>0$ and $\\alpha>0$. When the matrix size $n\\to\\infty$, we obtain an asymptotic formula for the Hankel determinants, valid uniformly for $t\\in (0, d]$, $d>0$ fixed. A particular Painlev\\'{e} III transcendent is involved in the approximation, as well as in the large-$n$ asymptotics of the leading coefficients and recurrence coefficients for the corresponding perturbed Laguerre polynomials. The derivation is based on the asymptotic results i"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1407.7334","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"}