{"paper":{"title":"Distribution of Schmidt-like eigenvalues for Gaussian Ensembles of the Random Matrix Theory","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cond-mat.stat-mech"],"primary_cat":"cond-mat.dis-nn","authors_text":"(2) LPTMC, Brazil, France), G. Oshanin (2) ((1) Instituto de Fisica, Marie Curie, M. P. Pato (1), Paris, Universidade de Sao Paulo, University Pierre","submitted_at":"2012-10-10T13:13:17Z","abstract_excerpt":"We analyze the form of the probability distribution function P_{n}^{(\\beta)}(w) of the Schmidt-like random variable w = x_1^2/(\\sum_{j=1}^n x^{2}_j/n), where x_j are the eigenvalues of a given n \\times n \\beta-Gaussian random matrix, \\beta being the Dyson symmetry index. This variable, by definition, can be considered as a measure of how any individual eigenvalue deviates from the arithmetic mean value of all eigenvalues of a given random matrix, and its distribution is calculated with respect to the ensemble of such \\beta-Gaussian random matrices. We show that in the asymptotic limit n \\to \\i"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1210.2904","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"}