{"paper":{"title":"Heat Kernel Empirical Laws on $\\mathbb{U}_N$ and $\\mathbb{GL}_N$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.FA"],"primary_cat":"math.PR","authors_text":"Todd Kemp","submitted_at":"2013-06-10T08:50:52Z","abstract_excerpt":"This paper studies the empirical measures of eigenvalues and singular values for random matrices drawn from the heat kernel measures on the unitary groups $\\mathbb{U}_N$ and the general linear groups $\\mathbb{GL}_N$, for $N\\in\\mathbb{N}$. It establishes the strongest known convergence results for the empirical eigenvalues in the $\\mathbb{U}_N$ case, and the first known almost sure convergence results for the eigenvalues and singular values in the $\\mathbb{GL}_N$ case. The limit noncommutative distribution associated to the heat kernel measure on $\\mathbb{GL}_N$ is identified as the projection "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1306.2140","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"}