{"paper":{"title":"Eigenvalues of Hermite and Laguerre ensembles: Large Beta Asymptotics","license":"","headline":"","cross_cats":["math.MP"],"primary_cat":"math-ph","authors_text":"Alan Edelman, Ioana Dumitriu","submitted_at":"2004-03-16T20:02:39Z","abstract_excerpt":"In this paper we examine the zero and first order eigenvalue fluctuations for the $\\beta$-Hermite and $\\beta$-Laguerre ensembles, using the matrix models we described in \\cite{dumitriu02}, in the limit as $\\beta \\to \\infty$. We find that the fluctuations are described by Gaussians of variance $O(1/\\beta)$, centered at the roots of a corresponding Hermite (Laguerre) polynomial. We also show that the approximation is very good, even for small values of $\\beta$, by plotting exact level densities versus sum of Gaussians approximations."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math-ph/0403029","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"}