{"paper":{"title":"Interior eigenvalue density of Jordan matrices with random perturbations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.SP","authors_text":"Johannes Sjoestrand, Martin Vogel","submitted_at":"2014-12-06T12:52:43Z","abstract_excerpt":"We study the eigenvalue distribution of a large Jordan block subject to a small random Gaussian perturbation. A result by E.B. Davies and M. Hager shows that as the dimension of the matrix gets large, with probability close to $1$, most of the eigenvalues are close to a circle. We study the expected eigenvalue density of the perturbed Jordan block in the interior of that circle and give a precise asymptotic description."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1412.2230","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"}