{"paper":{"title":"Universality for random matrices with an edge spectrum singularity","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CA","math.MP","nlin.SI"],"primary_cat":"math-ph","authors_text":"Thomas Bothner, Toby Shepherd","submitted_at":"2024-11-27T17:51:23Z","abstract_excerpt":"We study invariant random matrix ensembles \\begin{equation*}\n  \\mathbb{P}_n(d M)=Z_n^{-1}\\exp(-n\\,tr(V(M)))\\,d M \\end{equation*} defined on complex Hermitian matrices $M$ of size $n\\times n$, where $V$ is real analytic such that the underlying density of states is one-cut regular. Considering the average \\begin{equation*}\n  E_n[\\phi;\\lambda,\\alpha,\\beta]:=\\mathbb{E}_n\\bigg(\\prod_{\\ell=1}^n\\big(1-\\phi(\\lambda_{\\ell}(M))\\big)\\omega_{\\alpha\\beta}(\\lambda_{\\ell}(M)-\\lambda)\\bigg),\\ \\ \\ \\ \\ \\omega_{\\alpha\\beta}(x):=|x|^{\\alpha}\\begin{cases}1,&x<0\\\\ \\beta,&x\\geq 0\\end{cases}, \\end{equation*} taken w"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2411.18550","kind":"arxiv","version":2},"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/2411.18550/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"}