{"paper":{"title":"Universality of the ESD for a fixed matrix plus small random noise: a stability approach","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Philip Matchett Wood","submitted_at":"2014-03-18T19:56:35Z","abstract_excerpt":"We study the empirical spectral distribution (ESD) in the limit where n goes to infinity of a fixed n by n matrix M_n plus small random noise of the form f(n)X_n, where X_n has iid mean 0, variance 1/n entries and f(n) goes to 0 as n goes to infinity. It is known for certain M_n, in the case where X_n is iid complex Gaussian, that the limiting distribution of the ESD of M_n+f(n)X_n can be dramatically different from that for M_n. We prove a general universality result showing, with some conditions on M_n and f(n), that the limiting distribution of the ESD does not depend on the type of distrib"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1403.4593","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"}