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On the Eigenvalues of Random Matrices.
Linear Functionals of Eigenvalues of Random Matrices
Random unitary matrix the calculation function
2015/7/14
.L.et 1% be a random r~x r~unitary matrix with distribution given
by Haar measure on the unitary group. Using explicit monlerlt calculations,
a general criterion is given for linear cornbinations of...
Random Matrices, Magic Squares and Matching Polynomials
Random matrix the rubik's cube matching polynomial
2015/7/8
Random Matrices, Magic Squares and Matching Polynomials。
Random matrices: Universality of local spectral statistics of non-Hermitian matrices
Random matrices non-Hermitian matrices Probability
2012/6/30
It is a classical result of Ginibre that the normalized bulk $k$-point correlation functions of a complex $n \times n$ gaussian matrix with independent entries of mean zero and unit variance are asymp...
The circular law asserts that the spectral measure of eigenvalues of rescaled random matrices without symmetry assumption converges to the uniform measure on the unit disk. We prove a local version of...
On High Moments and the Spectral Norm of Large Dilute Wigner Random Matrices
random matrices Wigner ensemble dilute random matrices
2011/9/22
Abstract: We consider a dilute version of the Wigner ensemble of n-dimensional random matrices H such that each row has in average \rho_n non-zero elements. We study asymptotic properties of the spect...
Induced Ginibre ensemble of random matrices and quantum operations
Induced Ginibre ensemble random matrices quantum operations
2011/9/20
Abstract: A generalisation of the Ginibre ensemble of non-Hermitian random square matrices is introduced. The corresponding probability measure is induced by the ensemble of rectangular Gaussian matri...
On the Spectra and Pseudospectra of a Class of Non-Self-Adjoint Random Matrices and Operators
Pseudospectra Non-Self-Adjoint Random Matrices Operators
2011/8/22
Abstract: In this paper we develop and apply methods for the spectral analysis of non-self-adjoint tridiagonal infinite and finite random matrices, and for the spectral analysis of analogous determini...
A CLT for Information-theoretic statistics of Non-centered Gram random matrices
Random Matrix Spectral measure Stieltjes Transform Central Limit Theorem
2011/8/22
Abstract: In this article, we study the fluctuations of the random variable: $$ {\mathcal I}_n(\rho) = \frac 1N \log\det(\Sigma_n \Sigma_n^* + \rho I_N),\quad (\rho>0) $$ where $\Sigma_n= n^{-1/2} D_n...
Universality of local spectral statistics of random matrices
Random matrix Local semicircle law Tracy-Widom distribution Dyson Brownian motion
2011/7/28
Abstract: The Wigner-Gaudin-Mehta-Dyson conjecture asserts that the local eigenvalue statistics of large random matrices exhibit universal behavior depending only on the symmetry class of the matrix e...
The Continuum Limit of Toda Lattices for Random Matrices with Odd Weights
Toda Lattices Continuum Limit Random Matrices Odd Weights
2011/7/7
This paper is concerned with the asymptotic behavior of the free energy for a class of Hermitean random matrix models, with odd degree polynomial potential, in the large N limit. It continues an inves...
The Continuum Limit of Toda Lattices for Random Matrices with Odd Weights
The Continuum Limit of Toda Lattices Random Matrices Odd Weights
2011/7/25
Abstract: This paper is concerned with the asymptotic behavior of the free energy for a class of Hermitean random matrix models, with odd degree polynomial potential, in the large N limit. It continue...
Asymmetric random matrices: What do we need them for?
Asymmetric random matrices Complexity and matrices
2011/8/26
Complex systems are typically represented by large ensembles of observations.Correlation matrices provide an efficient formal framework to extract information from such multivariate ensembles and iden...
Fluctuations of Matrix Entries of Regular Functions of Sample Covariance Random Matrices
Matrix Entries Sample Covariance Random Matrices Probability
2011/7/27
Abstract: We extend the results about the fluctuations of the matrix entries of regular functions of Wigner matrices to the case of sample covariance random matrices.
Singularity of Random Matrices over Finite Fields
Singularity of Random Matrices Finite Fields
2011/1/20
Let A be an n×n random matrix with iid entries over a finite field of order q. Suppose that the entries do not take values in any additive coset of the field with probability greater than 1 − ...