{"paper":{"title":"Large deviations principle for the largest eigenvalue of 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":"2018-06-20T10:27:37Z","abstract_excerpt":"We consider the Gaussian beta-ensemble when $\\beta$ scales with $n$ the number of particles such that $\\displaystyle{{n}^{-1}\\ll \\beta\\ll 1}$. Under a certain regime for $\\beta$, we show that the largest particle satisfies a large deviations principle in $\\mathbb{R}$ with speed $n\\beta$ and explicit rate function. As a consequence, the largest particle converges in probability to $2$, the rightmost point of the semicircle law."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1806.07651","kind":"arxiv","version":4},"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"}