{"paper":{"title":"CLT for fluctuations of linear statistics in the Sine-beta process","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP"],"primary_cat":"math.PR","authors_text":"Thomas Lebl\\'e","submitted_at":"2018-09-10T16:37:43Z","abstract_excerpt":"We prove, for any $\\beta >0$, a central limit theorem for the fluctuations of linear statistics in the Sine-$\\beta$ process, which is the infinite volume limit of the random microscopic behavior in the bulk of one-dimensional log-gases at inverse temperature $\\beta$. If $\\phi$ is a compactly supported test function of class $C^4$, and $\\mathcal{C}$ is a random point configuration distributed according to Sine-$\\beta$, the integral of $\\phi(\\cdot / \\ell)$ against the random fluctuation $d\\mathcal{C} - dx$, converges in law, as $\\ell$ goes to infinity, to a centered normal random variable whose "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1809.03448","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"}