scholarly journals High moments of large Wigner random matrices and asymptotic properties of the spectral norm

2012 ◽  
Vol 20 (1) ◽  
Author(s):  
Oleksiy Khorunzhiy
Keyword(s):  
Random Matrices ◽  
Asymptotic Properties ◽  
Spectral Norm ◽  
Wigner Random Matrices

scholarly journals Asymptotic properties of large random matrices with independent entries

1996 ◽  
Vol 37 (10) ◽  
pp. 5033-5060 ◽  
Author(s):  
Alexei M. Khorunzhy ◽  
Boris A. Khoruzhenko ◽  
Leonid A. Pastur
Keyword(s):  
Random Matrices ◽  
Asymptotic Properties

scholarly journals ON FINITE RANK DEFORMATIONS OF WIGNER MATRICES II: DELOCALIZED PERTURBATIONS

2013 ◽  
Vol 02 (01) ◽  
pp. 1250015 ◽  
Author(s):  
DAVID RENFREW ◽  
ALEXANDER SOSHNIKOV
Keyword(s):  
Random Matrices ◽  
Finite Rank ◽  
Fourth Moment ◽  
Wigner Matrices ◽  
Wigner Random Matrices ◽  
The Matrix

We study the distribution of the outliers in the spectrum of finite rank deformations of Wigner random matrices. We assume that the matrix entries have finite fourth moment and extend the results by Capitaine, Donati-Martin, and Féral for perturbations whose eigenvectors are delocalized.

scholarly journals EIGENVALUE VARIANCE BOUNDS FOR WIGNER AND COVARIANCE RANDOM MATRICES

2012 ◽  
Vol 01 (03) ◽  
pp. 1250007 ◽  
Author(s):  
S. DALLAPORTA
Keyword(s):  
Random Matrices ◽  
Spectral Measure ◽  
Wasserstein Distance ◽  
Covariance Matrices ◽  
Finite Range ◽  
Variance Bounds ◽  
Semicircle Law ◽  
Wigner Matrices ◽  
Wigner Random Matrices

This work is concerned with finite range bounds on the variance of individual eigenvalues of Wigner random matrices, in the bulk and at the edge of the spectrum, as well as for some intermediate eigenvalues. Relying on the GUE example, which needs to be investigated first, the main bounds are extended to families of Hermitian Wigner matrices by means of the Tao and Vu Four Moment Theorem and recent localization results by Erdös, Yau and Yin. The case of real Wigner matrices is obtained from interlacing formulas. As an application, bounds on the expected 2-Wasserstein distance between the empirical spectral measure and the semicircle law are derived. Similar results are available for random covariance matrices.

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