{"paper":{"title":"A note on eigenvalues of random block Toeplitz matrices with slowly growing bandwidth","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Dang-Zheng Liu, Xin Sun, Yi-Ting Li, Zheng-Dong Wang","submitted_at":"2011-08-13T18:18:23Z","abstract_excerpt":"This paper can be thought of as a remark of \\cite{llw}, where the authors studied the eigenvalue distribution $\\mu_{X_N}$ of random block Toeplitz band matrices with given block order $m$. In this note we will give explicit density functions of $\\lim\\limits_{N\\to\\infty}\\mu_{X_N}$ when the bandwidth grows slowly. In fact, these densities are exactly the normalized one-point correlation functions of $m\\times m$ Gaussian unitary ensemble (GUE for short). The series $\\{\\lim\\limits_{N\\to\\infty}\\mu_{X_N}|m\\in\\mathbb{N}\\}$ can be seen as a transition from the standard normal distribution to semicircl"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1108.2810","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"}