{"paper":{"title":"Large deviation principle for the largest eigenvalue of random matrices with a variance profile","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Alice Guionnet, Jonathan Husson, Rapha\\\"el Ducatez","submitted_at":"2024-03-08T16:13:33Z","abstract_excerpt":"We establish large deviation principles for the largest eigenvalue of large random matrices with variance profiles. For $N \\in \\mathbb N$, we consider random $N \\times N$ symmetric matrices $H^N$ which are such that $H_{ij}^{N}=\\frac{1}{\\sqrt{N}}X_{i,j}^{N}$ for $1 \\leq i,j \\leq N$, where the $X_{i,j}^{N}$ for $1 \\leq i \\leq j \\leq N$ are independent and centered. We then denote $\\Sigma_{i,j} ^N = \\text{Var} (X_{i,j}^{N}) ( 1 + \\textbf{1}_{ i =j})^{-1}$ the variance profile of $H^N$. Our large deviation principle is then stated under the assumption that the $\\Sigma^N$ converge in a certain sen"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2403.05413","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/2403.05413/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"}