{"paper":{"title":"Sharp deviation inequalities for the 2D Coulomb gas and Quantum hall states, I","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CV","math.MP","math.PR"],"primary_cat":"math-ph","authors_text":"Robert J. Berman","submitted_at":"2019-06-20T09:54:24Z","abstract_excerpt":"We establish sharp deviation inequalities for the linear statistics of the 2D Coulomb gas. These imply sub-Gaussian inequalities, where the variance is given by the Dirichlet norm. The proofs use complex geometry and potential theory on Riemann surfaces and apply more generally to beta-ensembles, which also include integer Quantum Hall states on Riemann surfaces. In a sequel of the paper we give applications to large and moderate deviation principles, local laws at mesoscopic scales, quantitative Bergman kernel asymptotics. In a series of companion papers applications to concentration of measu"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1906.08529","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"}