Statistics of infinite dimensional random matrix ensembles
نویسنده
چکیده
A complex quantum system with energy dissipation is considered. The quantum Hamiltonians H belong the complex Ginibre ensemble. The complex-valued eigenenergies Zi are random variables. The second differences ∆Zi are also complex-valued random variables. The second differences have their real and imaginary parts and also radii (moduli) and main arguments (angles). For N=3 dimensional Ginibre ensemble the distributions of above random variables are provided whereas for generic N dimensional Ginibre ensemble second difference distribution is analytically calculated. The law of homogenization of eigenergies is formulated. The analogy of Wigner and Dyson of Coulomb gas of electric charges is studied.
منابع مشابه
Poisson Statistics for the Largest Eigenvalues in Random Matrix Ensembles
The two archetypal ensembles of random matrices are Wigner real symmetric (Hermitian) random matrices and Wishart sample covariance real (complex) random matrices. In this paper we study the statistical properties of the largest eigenvalues of such matrices in the case when the second moments of matrix entries are infinite. In the first two subsections we consider Wigner ensemble of random matr...
متن کاملConformal Deformation from Normal to Hermitian Random Matrix Ensembles
We investigate the eigenvalues statistics of ensembles of normal randommatrices when their order N tends to infinite. In the model the eigenvalues have uniform density within a region determined by a simple analytic polynomial curve. We study the conformal deformations of normal random ensembles to Hermitian random ensembles and give sufficient conditions for the latter to be a Wigner ensemble.
متن کاملEigenvalue Statistics for Cmv Matrices: from Poisson to Clock via Random Matrix Ensembles
We study CMV matrices (discrete one-dimensional Dirac-type operators) with random decaying coefficients. Under mild assumptions we identify the local eigenvalue statistics in the natural scaling limit. For rapidly decreasing coefficients, the eigenvalues have rigid spacing (like the numerals on a clock); in the case of slow decrease, the eigenvalues are distributed according to a Poisson proces...
متن کاملOn Compressive Ensemble Induced Regularisation: How Close is the Finite Ensemble Precision Matrix to the Infinite Ensemble?
Averaging ensembles of randomly oriented low-dimensional projections of a singular covariance represent a novel and attractive means to obtain a well-conditioned inverse, which only needs access to random projections of the data. However, theoretical analyses so far have only been done at convergence, implying good properties for ‘large-enough’ ensembles. But how large is ‘large enough’? Here w...
متن کاملOn the similarity between Nakagami-m Fading distribution and the Gaussian ensembles of random matrix theory
We report the similarity between the Nakagami-m fading distribution and the three Gaussian ensembles of random matrix theory. We provide a brief review of random matrix theory and wireless fading. We show that the Nakagami-m distribution serves as mapping between the three ensembles. The statistics of the wireless fading amplitude, as modeled by Nakagami-m distribution, provide a rare example o...
متن کامل