{"paper":{"title":"Random matrices have simple spectrum","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO"],"primary_cat":"math.PR","authors_text":"Terence Tao, Van Vu","submitted_at":"2014-12-03T18:49:47Z","abstract_excerpt":"Let $M_n = (\\xi_{ij})_{1 \\leq i,j \\leq n}$ be a real symmetric random matrix in which the upper-triangular entries $\\xi_{ij}, i<j$ and diagonal entries $\\xi_{ii}$ are independent. We show that with probability tending to 1, $M_n$ has no repeated eigenvalues. As a corollary, we deduce that the Erd{\\H o}s-Renyi random graph has simple spectrum asymptotically almost surely, answering a question of Babai."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1412.1438","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"}