Level spacings distribution for large random matrices: Gaussian fluctuations

• 成果类型: Article
• 署名作者: Soshnikov, A
• 刊物名称: ANNALS OF MATHEMATICS
• ISSN/ISSBN: 0003-486X
• DOI: 10.2307/121004
• 发表日期: 1998
• 页码: 573-617
• 关键词: universality; eigenvalues; zeros

摘要

We study the level-spacings distribution for eigenvalues of large N x N matrices from the classical compact groups in the scaling limit when the mean distance between nearest eigenvalues equals 1. Defining by eta(N)(s) the number of nearest neighbors spacings greater than s > 0 (smaller than s > 0) we prove functional limit theorem for the process (eta(N)(s) - E eta(N)(s))/N-1/2, giving weak convergence of this distribution to some Gaussian random process on [0, infinity). The limiting Gaussian random process is universal for all classical compact groups. It is Holder continuous with any exponent less than 1/2. Similar results can be obtained for the n-level-spacings distribution.