Local spectrum of truncations of Kronecker products of Haar distributed unitary matrices
نویسندگان
چکیده
منابع مشابه
Local Spectrum of Truncations of Kronecker Products of Haar Distributed Unitary Matrices
We address the local spectral behavior of the random matrix Π1U ⊗kΠ2U ⊗k∗Π1, where U is a Haar distributed unitary matrix of size n×n, the factor k is at most c0 logn for a small constant c0 > 0, and Π1,Π2 are arbitrary projections on l n k 2 of ranks proportional to n. We prove that in this setting the k-fold Kronecker product behaves similarly to the well-studied case when k = 1. AMS Subject ...
متن کاملHaar-Distributed Unitary Matrices
We provide an elementary proof for a theorem due to Petz and Réffy which states that for a random n × n unitary matrix with distribution given by the Haar measure on the unitary group U(n), the upper left (or any other) k × k submatrix converges in distribution, after multiplying by a normalization factor √ n and as n → ∞, to a matrix of independent complex Gaussian random variables with mean 0...
متن کاملRandom Truncations of Haar Distributed Matrices and Bridges
Let U be a Haar distributed matrix in U(n) or O(n). In a previous paper, we proved that after centering, the two-parameter process T (s, t) = ∑ i≤⌊ns⌋,j≤⌊nt⌋ |Uij | 2 converges in distribution to the bivariate tied-down Brownian bridge. In the present paper, we replace the deterministic truncation of U by a random one, where each row (resp. column) is chosen with probability s (resp. t) indepen...
متن کاملTruncations of Haar Distributed Matrices, Traces and Bivariate Brownian Bridge
Let U be a Haar distributed matrix in U(n) or O(n). We show that after centering the two-parameter process W (s, t) = ∑ i≤⌊ns⌋,j≤⌊nt⌋ |Uij | 2 converges in distribution to the bivariate tied-down Brownian bridge.
متن کاملTruncations of Haar distributed matrices, traces and bivariate Brownian bridges
Let U be a Haar distributed matrix in U(n) or O(n). We show that after centering the two-parameter process W (s, t) = ∑ i≤⌊ns⌋,j≤⌊nt⌋ |Uij | 2 converges in distribution to the bivariate tied-down Brownian bridge.
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Random Matrices: Theory and Applications
سال: 2015
ISSN: 2010-3263,2010-3271
DOI: 10.1142/s201032631550001x