Limiting spectral distribution of the product of truncated Haar unitary matrices
نویسندگان
چکیده
منابع مشابه
Limiting spectral distribution of sums of unitary and orthogonal matrices∗
We show that the empirical eigenvalue measure for sum of d independent Haar distributed n-dimensional unitary matrices, converge for n → ∞ to the Brown measure of the free sum of d Haar unitary operators. The same applies for independent Haar distributed n-dimensional orthogonal matrices. As a byproduct of our approach, we relax the requirement of uniformly bounded imaginary part of Stieltjes t...
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Let Um be an m×m Haar unitary matrix and U[m,n] be its n×n truncation. In this paper the large deviation is proven for the empirical eigenvalue density of U[m,n] as m/n → λ and n → ∞. The rate function and the limit distribution are given explicitely. U[m,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....
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ژورنال
عنوان ژورنال: Random Matrices: Theory and Applications
سال: 2019
ISSN: 2010-3263,2010-3271
DOI: 10.1142/s2010326320500021