{"paper":{"title":"Extremes of Chi triangular array from the Gaussian $\\beta$-Ensemble at high temperature","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Cambyse Pakzad","submitted_at":"2019-03-05T23:10:26Z","abstract_excerpt":"We study the extreme point process associated to the off-diagonal components in the matrix representation of the Gaussian $\\beta$-Ensemble and prove its convergence to Poisson point process as $n\\to +\\infty$ when the inverse temperature $\\beta$ scales with $n$ and tends to $0$. We consider two main high temperature regimes: $\\displaystyle{\\beta\\ll \\frac{1}{n}}$ and $\\displaystyle{n\\beta= 2\\gamma \\geq 0}$. The normalizing sequences are explicitly given in each cases. As a consequence, we estimate the first order asymptotic of the largest eigenvalue of the Gaussian $\\beta$-Ensemble."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1903.02103","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"}