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Circular law for random discrete matrices of given row sum
 J. COMB
, 2012
"... Let Mn be a random matrix of size n×n and let λ1,..., λn be the eigenvalues of Mn. The empirical spectral distribution µMn of Mn is defined as µMn(s, t) = 1 n #{k ≤ n,<(λk) ≤ s;=(λk) ≤ t}. The circular law theorem in random matrix theory asserts that if the entries of Mn are i.i.d. copies of a ..."
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Let Mn be a random matrix of size n×n and let λ1,..., λn be the eigenvalues of Mn. The empirical spectral distribution µMn of Mn is defined as µMn(s, t) = 1 n #{k ≤ n,<(λk) ≤ s;=(λk) ≤ t}. The circular law theorem in random matrix theory asserts that if the entries of Mn are i.i.d. copies of a random variable with mean zero and variance σ2, then the empirical spectral distribution of the normalized matrix 1
The Spectrum of Random Kernel Matrices: Universality Results for Rough and Varying Kernels
 Random Matrices: Theory and Applications
, 2013
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Rouault Bridges and random truncations of random matrices Random Matrices
 Theory and Appl
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RANDOM TRUNCATIONS OF HAAR DISTRIBUTED MATRICES AND BRIDGES
, 2013
"... Abstract. Let U be a Haar distributed matrix in U(n) or O(n). In a previous paper, we proved that after centering, the twoparameter process T (n) (s,t) = Uij  2 i≤⌊ns⌋,j≤⌊nt⌋ converges in distribution to the bivariate tieddown Brownian bridge. In the present paper, we replace the deterministic t ..."
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Abstract. Let U be a Haar distributed matrix in U(n) or O(n). In a previous paper, we proved that after centering, the twoparameter process T (n) (s,t) = Uij  2 i≤⌊ns⌋,j≤⌊nt⌋ converges in distribution to the bivariate tieddown 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) independently. We prove that the corresponding twoparameter process, after centering and normalization by n −1/2 converges to a Gaussian process. On the way we meet other interesting convergences. 1.
2 A NOTE ON THE MARCHENKOPASTUR LAW FOR A CLASS OF RANDOM MATRICES WITH DEPENDENT ENTRIES
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