{"paper":{"title":"Regularization of non-normal matrices by Gaussian noise - the banded Toeplitz and twisted Toeplitz cases","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Anirban Basak, Elliot Paquette, Ofer Zeitouni","submitted_at":"2017-11-30T19:31:38Z","abstract_excerpt":"We consider the spectrum of additive, polynomially vanishing random perturbations of deterministic matrices, as follows. Let $M_N$ be a deterministic $N\\times N$ matrix, and let $G_N$ be a complex Ginibre matrix. We consider the matrix $\\mathcal{M}_N=M_N+N^{-\\gamma}G_N$, where $\\gamma>1/2$. With $L_N$ the empirical measure of eigenvalues of $\\mathcal{M}_N$, we provide a general deterministic equivalence theorem that ties $L_N$ to the singular values of $z-M_N$, with $z\\in \\mathbb{C}$. We then compute the limit of $L_N$ when $M_N$ is an upper triangular Toeplitz matrix of finite symbol: if $M_N"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1712.00042","kind":"arxiv","version":3},"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"}