{"paper":{"title":"Finite N Fluctuation Formulas for Random Matrices","license":"","headline":"","cross_cats":[],"primary_cat":"cond-mat.stat-mech","authors_text":"P. J. Forrester (Uni. of Melbourne), T. H. Baker","submitted_at":"1997-01-19T12:34:50Z","abstract_excerpt":"For the Gaussian and Laguerre random matrix ensembles, the probability density function (p.d.f.) for the linear statistic $\\sum_{j=1}^N (x_j - <x>)$ is computed exactly and shown to satisfy a central limit theorem as $N \\to \\infty$. For the circular random matrix ensemble the p.d.f.'s for the linear statistics ${1 \\over 2} \\sum_{j=1}^N (\\theta_j - \\pi)$ and $- \\sum_{j=1}^N \\log 2|\\sin \\theta_j/2|$ are calculated exactly by using a constant term identity from the theory of the Selberg integral, and are also shown to satisfy a central limit theorem as $N \\to \\infty$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"cond-mat/9701133","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"}