{"paper":{"title":"Large deviations of the top eigenvalue of large Cauchy random matrices","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP"],"primary_cat":"cond-mat.stat-mech","authors_text":"Dario Villamaina, Gregory Schehr, Pierpaolo Vivo, Satya N. Majumdar","submitted_at":"2012-10-19T12:32:18Z","abstract_excerpt":"We compute analytically the probability density function (pdf) of the largest eigenvalue $\\lambda_{\\max}$ in rotationally invariant Cauchy ensembles of $N\\times N$ matrices. We consider unitary ($\\beta = 2$), orthogonal ($\\beta =1$) and symplectic ($\\beta=4$) ensembles of such heavy-tailed random matrices. We show that a central non-Gaussian regime for $\\lambda_{\\max} \\sim \\mathcal{O}(N)$ is flanked by large deviation tails on both sides which we compute here exactly for any value of $\\beta$. By matching these tails with the central regime, we obtain the exact leading asymptotic behaviors of t"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1210.5400","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"}