{"paper":{"title":"Extreme eigenvalues of sparse, heavy tailed random matrices","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Antonio Auffinger, Si Tang","submitted_at":"2015-06-19T22:48:36Z","abstract_excerpt":"We study the statistics of the largest eigenvalues of $p \\times p$ sample covariance matrices $\\Sigma_{p,n} = M_{p,n}M_{p,n}^{*}$ when the entries of the $p \\times n$ matrix $M_{p,n}$ are sparse and have a distribution with tail $t^{-\\alpha}$, $\\alpha>0$. On average the number of nonzero entries of $M_{p,n}$ is of order $n^{\\mu+1}$, $0 \\leq \\mu \\leq 1$. We prove that in the large $n$ limit, the largest eigenvalues are Poissonian if $\\alpha<2(1+\\mu^{{-1}})$ and converge to a constant in the case $\\alpha>2(1+\\mu^{{-1}})$. We also extend the results of Benaych-Georges and Peche [7] in the Hermiti"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1506.06175","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"}