{"paper":{"title":"Higher order large gap asymptotics at the hard edge for Muttalib--Borodin ensembles","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.MP"],"primary_cat":"math-ph","authors_text":"Christophe Charlier, Jonatan Lenells, Julian Mauersberger","submitted_at":"2019-06-28T11:01:55Z","abstract_excerpt":"We consider the limiting process that arises at the hard edge of Muttalib--Borodin ensembles. This point process depends on $\\theta > 0$ and has a kernel built out of Wright's generalized Bessel functions. In a recent paper, Claeys, Girotti and Stivigny have established first and second order asymptotics for large gap probabilities in these ensembles. These asymptotics take the form \\begin{equation*} \\mathbb{P}(\\mbox{gap on } [0,s]) = C \\exp \\left( -a s^{2\\rho} + b s^{\\rho} + c \\ln s \\right) (1 + o(1)) \\qquad \\mbox{as }s \\to + \\infty, \\end{equation*} where the constants $\\rho$, $a$, and $b$ ha"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1906.12130","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"}