{"paper":{"title":"Dyson Brownian Motion for General $\\beta$ and Potential at the Edge","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Arka Adhikari, Jiaoyang Huang","submitted_at":"2018-10-18T23:42:22Z","abstract_excerpt":"In this paper, we compare the solutions of Dyson Brownian motion with general $\\beta$ and potential $V$ and the associated McKean-Vlasov equation near the edge. Under suitable conditions on the initial data and potential $V$, we obtain the optimal rigidity estimates of particle locations near the edge for short time $t=\\text{o}(1)$. Our argument uses the method of characteristics along with a careful estimate involving an equation of the edge. With the rigidity estimates as an input, we prove a central limit theorem for mesoscopic statistics near the edge which, as far as we know, have been do"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1810.08308","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"}