Large deviation for the empirical eigenvalue density of truncated Haar unitary matrices
成果类型：
Article
署名作者：
Petz, D; Réffy, J
署名单位：
Budapest University of Technology & Economics
刊物名称：
PROBABILITY THEORY AND RELATED FIELDS
ISSN/ISSBN：
0178-8051
DOI：
10.1007/s00440-004-0420-5
发表日期：
2005
页码：
175-189
关键词：
摘要：
Let U-m be an mxm Haar unitary matrix and U-[m,U-n] be its nxn truncation. In this paper the large deviation is proven for the empirical eigenvalue density of U-[m,U-n] as m/n -> lambda and n -> infinity. The rate function and the limit distribution are given explicitly. U-[m,U-n] is the random matrix model of quq, where u is a Haar unitary in a finite von Neumann algebra, q is a certain projection and they are free. The limit distribution coincides with the Brown measure of the operator quq.
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