{"paper":{"title":"Large deviations of the empirical spectral measure of supercritical sparse Wigner matrices","license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","headline":"","cross_cats":["math-ph","math.CO","math.MP"],"primary_cat":"math.PR","authors_text":"Fanny Augeri","submitted_at":"2024-01-22T13:12:46Z","abstract_excerpt":"Let $\\Xi$ be the adjacency matrix of an Erd\\H{o}s-R\\'enyi graph on $n$ vertices and with parameter $p$ and consider $A$ a $n\\times n$ centered random symmetric matrix with bounded i.i.d. entries above the diagonal. When the mean degree $np$ diverges, the empirical spectral measure of the normalized Hadamard product $(A \\circ \\Xi)/\\sqrt{np}$ converges weakly in probability to the semicircle law. In the regime where $p\\ll 1$ and $ np \\gg \\log n$, we prove a large deviations principle for the empirical spectral measure with speed $n^2p$ and with a good rate function solution of a certain variatio"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2401.11925","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2401.11925/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"}