{"paper":{"title":"Sanov-type large deviations in Schatten classes","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.FA"],"primary_cat":"math.PR","authors_text":"Christoph Thaele, Joscha Prochno, Zakhar Kabluchko","submitted_at":"2018-08-14T19:04:26Z","abstract_excerpt":"Denote by $\\lambda_1(A), \\ldots, \\lambda_n(A)$ the eigenvalues of an $(n\\times n)$-matrix $A$. Let $Z_n$ be an $(n\\times n)$-matrix chosen uniformly at random from the matrix analogue to the classical $\\ell_ p^n$-ball, defined as the set of all self-adjoint $(n\\times n)$-matrices satisfying $\\sum_{k=1}^n |\\lambda_k(A)|^p\\leq 1$. We prove a large deviations principle for the (random) spectral measure of the matrix $n^{1/p} Z_n$. As a consequence, we obtain that the spectral measure of $n^{1/p} Z_n$ converges weakly almost surely to a non-random limiting measure given by the Ullman distribution,"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1808.04862","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"}