{"paper":{"title":"Large deviations of crowding in finite $\\beta$-ensembles","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Kartick Adhikari, Sitanath Majumder","submitted_at":"2026-05-18T10:37:58Z","abstract_excerpt":"We consider finite $\\beta$-ensembles $\\mathcal X_{n,\\beta}^{\\mathbb F}$ with $n$ points on $\\mathbb F$, where $\\mathbb F$ denotes either the real line or the complex plane. Let $U$ be a bounded subset of $ \\mathbb F$ such that $\\partial U$ (the boundary of $U$) is polar for $\\mathbb F=\\mathbb R$ and $\\partial U$ is a closed $1$--rectifiable set with finite $1$-dimensional Hausdorff measure. Suppose $\\mathcal X_{n,\\beta}^{\\mathbb F}(U)$ denotes the number of points in the region $U$. We show that the sequence of laws of $\\{n^{-1}\\mathcal X_{n,\\beta}^{\\mathbb F}(U); n\\ge 1\\}$ satisfies the large"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2605.18198","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2605.18198/integrity.json","findings":[],"available":true,"detectors_run":[{"name":"claim_evidence","ran_at":"2026-05-19T23:41:58.997062Z","status":"completed","version":"1.0.0","findings_count":0},{"name":"ai_meta_artifact","ran_at":"2026-05-19T23:33:35.324461Z","status":"skipped","version":"1.0.0","findings_count":0}],"snapshot_sha256":"1e7efdecb9133111f8aa961b17ad85b91a53519252006a92040465e58ba660fc"},"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"}