{"paper":{"title":"From gap probabilities in random matrix theory to eigenvalue expansions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.MP","math.PR","math.SP","nlin.SI"],"primary_cat":"math-ph","authors_text":"Thomas Bothner","submitted_at":"2015-09-23T21:06:24Z","abstract_excerpt":"We present a method to derive asymptotics of eigenvalues for trace-class integral operators $K:L^2(J;d\\lambda)\\circlearrowleft$, acting on a single interval $J\\subset\\mathbb{R}$, which belong to the ring of integrable operators \\cite{IIKS}. Our emphasis lies on the behavior of the spectrum $\\{\\lambda_i(J)\\}_{i=0}^{\\infty}$ of $K$ as $|J|\\rightarrow\\infty$ and $i$ is fixed. We show that this behavior is intimately linked to the analysis of the Fredholm determinant $\\det(I-\\gamma K)|_{L^2(J)}$ as $|J|\\rightarrow\\infty$ and $\\gamma\\uparrow 1$ in a Stokes type scaling regime. Concrete asymptotic f"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1509.07159","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"}