{"paper":{"title":"2D Coulomb Gases and the Renormalized Energy","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.MP","math.PR"],"primary_cat":"math-ph","authors_text":"Etienne Sandier, Sylvia Serfaty","submitted_at":"2012-01-17T12:56:50Z","abstract_excerpt":"We study the statistical mechanics of classical two-dimensional \"Coulomb gases\" with general potential and arbitrary \\beta, the inverse of the temperature. Such ensembles also correspond to random matrix models in some particular cases. The formal limit case \\beta=\\infty corresponds to \"weighted Fekete sets\" and also falls within our analysis.\n  It is known that in such a system points should be asymptotically distributed according to a macroscopic \"equilibrium measure,\" and that a large deviations principle holds for this, as proven by Ben Arous and Zeitouni.\n  By a suitable splitting of the "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1201.3503","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"}