{"paper":{"title":"Regularization of non-normal matrices by Gaussian noise","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Elliot Paquette, Ofer Zeitouni, Ohad Feldheim","submitted_at":"2014-04-14T08:32:19Z","abstract_excerpt":"We consider the regularization of matrices $M^N$ written in Jordan form by additive Gaussian noise $N^{-\\gamma}G^N$, where $G^N$ is a matrix of i.i.d. standard Gaussians and $\\gamma>1/2$ so that the operator norm of the additive noise tends to $0$ with $N$. Under mild conditions on the structure of $M^N$ we evaluate the limit of the empirical measure of eigenvalues of $M^N+N^{-\\gamma} G^N$ and show that it depends on $\\gamma$, in contrast with the case of a single Jordan block."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1404.3491","kind":"arxiv","version":2},"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"}