{"paper":{"title":"A Sudakov--Fernique proof of Lehner-type edge bounds for matrix-valued GUE sums","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math.OA"],"primary_cat":"math.PR","authors_text":"Benoit Collins, Yuta Yamagishi","submitted_at":"2026-06-19T06:22:37Z","abstract_excerpt":"Let $A_0,A_1,\\ldots,A_n\\in M_N(\\mathbb{C})$ be Hermitian matrices and let $G_1,\\ldots,G_n$ be independent $M\\times M$ GUE matrices normalized so that $\\|M^{-1/2}G_i\\|\\to 2$ almost surely as $M\\to\\infty$. We study the spectral edges and operator norm of $H_M = A_0\\otimes I_M + \\frac{1}{\\sqrt{M}}\\sum_{i=1}^n A_i\\otimes G_i$. Lehner's formula identifies the right and left edges of the corresponding free semicircular operator as $\\rho_+ = \\inf_{Z\\succ 0}\\lambda_{\\max}(A_0+Z+\\sum_{i=1}^n A_iZ^{-1}A_i)$ and $\\rho_- = \\sup_{Z\\prec 0}\\lambda_{\\min}(A_0+Z+\\sum_{i=1}^n A_iZ^{-1}A_i)$. Assuming $A_i\\succ"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.21137","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/2606.21137/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"}