MULTIVARIATE NORMAL APPROXIMATION FOR TRACES OF RANDOM UNITARY MATRICES

• 成果类型: Article
• 署名作者: Johansson, Kurt; Lambert, Gaultier
• 署名单位: Royal Institute of Technology; University of Zurich
• 刊物名称: ANNALS OF PROBABILITY
• ISSN/ISSBN: 0091-1798
• DOI: 10.1214/21-AOP1520
• 发表日期: 2021
• 页码: 2961-3010
• 关键词: toeplitz determinants; eigenvalues; FORMULA; borodin

摘要

In this article we obtain a superexponential rate of convergence in total variation between the traces of the first m powers of a n x n random unitary matrices and a 2m-dimensional Gaussian random variable. This generalizes previous results in the scalar case to the multivariate setting, and we also give the precise dependence on the dimensions m and n in the estimates with explicit constants. We are especially interested in the regime where m grows with n and our main result basically states that if m <