{"paper":{"title":"Gaussian beta ensembles: the perfect freezing transition and its characterization in terms of Beurling-Landau densities","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.CV","math.MP"],"primary_cat":"math.PR","authors_text":"Felipe Marceca, Jos\\'e Luis Romero, Yacin Ameur","submitted_at":"2022-05-30T12:36:26Z","abstract_excerpt":"The Gaussian $\\beta$-ensemble is a real $n$-point configuration $\\{x_j\\}_1^n$ picked randomly with respect to the Boltzmann factor $e^{-\\frac\\beta 2H_n}$, $H_n=\\sum_{i\\ne j}\\log\\frac 1{|x_i-x_j|}+n\\sum_{i=1}^n\\tfrac 12x_i^2.$ The point process $\\{x_j\\}_1^n$ tends to follow the semicircle law $\\sigma(x)=\\tfrac 1{2\\pi}\\sqrt{(4-x^2)_+}$ in certain average senses.\n  A Fekete configuration (minimizer of $H_n$) is spread out in a much more uniform way in the interval $[-2,2]$ with respect to the regularization $\\sigma_n(x)=\\max\\{\\sigma(x),n^{-\\frac 1 3}\\}$ of the semicircle law. In particular, Feket"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2205.15054","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2205.15054/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"}