{"paper":{"title":"Poisson statistics for matrix ensembles at large temperature","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Florent Benaych-Georges, Sandrine P\\'ech\\'e","submitted_at":"2015-06-10T21:49:41Z","abstract_excerpt":"In this article, we consider $\\beta$-ensembles, i.e. collections of particles with random positions on the real line having joint distribution $$\\frac{1}{Z_N(\\beta)}|\\Delta(\\lambda)|^\\beta e^{- \\frac{N\\beta}{4}\\sum_{i=1}^N\\lambda_i^2}d \\lambda,$$ in the regime where $\\beta\\to 0$ as $N\\to\\infty$. We briefly describe the global regime and then consider the local regime. In the case where $N\\beta$ stays bounded, we prove that the local eigenvalue statistics, in the vicinity of any real number, are asymptotically to those of a Poisson point process. In the case where $N\\beta\\to\\infty$, we prove a "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1506.03494","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"}