On random matrices from the compact classical groups
成果类型：
Article
署名作者：
Johansson, K
刊物名称：
ANNALS OF MATHEMATICS
ISSN/ISSBN：
0003-486X
DOI：
10.2307/2951843
发表日期：
1997
页码：
519-545
关键词：
摘要：
If M is a matrix taken randomly with respect to normalized Haar measure on U(n), O(n) or Sp(n), then the real and imaginary parts of the random variables Tr(M-k), k greater than or equal to 1, converge to independent normal random variables with mean zero and variance k/2, as the size n of the matrix goes to infinity. For the unitary group this is a direct consequence of the strong Szego theorem for Toeplitz determinants. We will prove a conjecture of Diaconis saying that for U(n) the rate of convergence to the limiting normal is O(n(-delta n)) for some delta > 0, and for O(n) and Sp(n) it is O(e(-cn)) for some c > 0.