{"paper":{"title":"On Wright's generalized Bessel kernel","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CA","math.MP","nlin.SI"],"primary_cat":"math-ph","authors_text":"Lun Zhang","submitted_at":"2016-08-09T16:58:17Z","abstract_excerpt":"In this paper, we consider the Wright's generalized Bessel kernel $K^{(\\alpha,\\theta)}(x,y)$ defined by $$\\theta x^{\\alpha}\\int_0^1J_{\\frac{\\alpha+1}{\\theta},\\frac{1}{\\theta}}(ux)J_{\\alpha+1,\\theta}((uy)^{\\theta})u^\\alpha\\,\\mathrm{d} u, \\qquad \\alpha>-1, \\qquad \\theta>0,$$ where $$J_{a,b}(x)=\\sum_{j=0}^\\infty\\frac{(-x)^j}{j!\\Gamma(a+bj)},\\qquad a\\in\\mathbb{C},\\qquad b>-1,$$ is Wright's generalization of the Bessel function. This non-symmetric kernel, which generalizes the classical Bessel kernel (corresponding to $\\theta=1$) in random matrix theory, is the hard edge scaling limit of the correl"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1608.02867","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"}