{"paper":{"title":"Curvature bound of Dyson Brownian Motion","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.DG","math.FA","math.MP"],"primary_cat":"math.PR","authors_text":"Kohei Suzuki","submitted_at":"2022-12-31T18:14:43Z","abstract_excerpt":"We construct a strongly local symmetric Dirichlet form on the configuration space $\\Upsilon$ whose symmetrising (thus also invariant) measure is $\\mathsf{sine}_\\beta$, which is the law of the sine $\\beta$ ensemble for every $\\beta>0$. For every $\\beta>0$, this Dirichlet form satisfies the Bakry-\\'Emery gradient estimate $\\mathsf{BE}(K, \\infty)$ with $K=0$. This implies various functional inequalities, including the local Poincar\\'e inequality, the local log-Sobolev inequality and the local hyper-contractivity. We then introduce an $L^2$-transportation-type extended distance $\\bar{\\sf d}_{\\Upsi"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2301.00262","kind":"arxiv","version":5},"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/2301.00262/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"}