{"paper":{"title":"Outliers in spectrum of sparse Wigner matrices","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO"],"primary_cat":"math.PR","authors_text":"Konstantin Tikhomirov, Pierre Youssef","submitted_at":"2019-04-16T21:03:27Z","abstract_excerpt":"In this paper, we study the effect of sparsity on the appearance of outliers in the semi-circular law. Let $(W_n)_{n=1}^\\infty$ be a sequence of random symmetric matrices such that each $W_n$ is $n\\times n$ with i.i.d entries above and on the main diagonal equidistributed with the product $b_n\\xi$, where $\\xi$ is a real centered uniformly bounded random variable of unit variance and $b_n$ is an independent Bernoulli random variable with a probability of success $p_n$. Assuming that $\\lim\\limits_{n\\to\\infty}n p_n=\\infty$, we show that for the random sequence $(\\rho_n)_{n=1}^\\infty$ given by $$\\"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1904.07985","kind":"arxiv","version":4},"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"}