{"paper":{"title":"Rigidity of Eigenvalues of Generalized Wigner Matrices","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.MP","math.PR"],"primary_cat":"math-ph","authors_text":"Horng-Tzer Yau, Jun Yin, Laszlo Erdos","submitted_at":"2010-07-27T09:44:30Z","abstract_excerpt":"Consider $N\\times N$ hermitian or symmetric random matrices $H$ with independent entries, where the distribution of the $(i,j)$ matrix element is given by the probability measure $\\nu_{ij}$ with zero expectation and with variance $\\sigma_{ij}^2$. We assume that the variances satisfy the normalization condition $\\sum_{i} \\sigma^2_{ij} = 1$ for all $j$ and that there is a positive constant $c$ such that $c\\le N \\sigma_{ij}^2 \\le c^{-1}$. We further assume that the probability distributions $\\nu_{ij}$ have a uniform subexponential decay. We prove that the Stieltjes transform of the empirical eige"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1007.4652","kind":"arxiv","version":7},"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"}