{"paper":{"title":"Universality for general Wigner-type matrices","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Laszlo Erdos, Oskari Ajanki, Torben Kr\\\"uger","submitted_at":"2015-06-16T19:55:17Z","abstract_excerpt":"We consider the local eigenvalue distribution of large self-adjoint $N\\times N$ random matrices $\\mathbf{H}=\\mathbf{H}^*$ with centered independent entries. In contrast to previous works the matrix of variances $s_{ij} = \\mathbb{E}\\, |h_{ij}|^2 $ is not assumed to be stochastic. Hence the density of states is not the Wigner semicircle law. Its possible shapes are described in the companion paper [1]. We show that as $N$ grows, the resolvent, $\\mathbf{G}(z)=(\\mathbf{H}-z)^{-1}$, converges to a diagonal matrix, $ \\mathrm{diag}(\\mathbf{m}(z)) $, where $\\mathbf{m}(z)=(m_1(z),\\dots,m_N(z))$ solves "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1506.05098","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"}