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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...
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
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.
On the high-density expansion for Euclidean Random Matrices
the high-density expansion Euclidean Random Matrices
2010/12/27
Diagrammatic techniques to compute perturbatively the spectral properties of Euclidean Random Matrices in the high-density regime are introduced and discussed in detail. Such techniques are developed ...
Typical rank of coin-toss power-law random matrices over GF(2)
Typical coin-toss power-law
2010/11/18
Random linear systems over the Galois Field modulo 2 have an interest in connection with problems ranging from computational op-timization to complex networks.
On the high-density expansion for Euclidean Random Matrices
high-density expansion Euclidean Random Matrices
2010/11/22
Diagrammatic techniques to compute perturbatively the spectral properties of Euclidean random
matrices (ERM) in the high-density regime are introduced and discussed in detail. Such techniques are dev...
I use quaternion free probability calculus - an extension of free probability to non-Hermitian matrices - to derive mean spectral densities of sums of independent (free) unitary random matrices in the...