Related papers: Constrained Eigenvalues Density of Invariant Rando…

We find the lattice spacing dependence of the eigenvalue density of the non-Hermitian Wilson Dirac operator in the $\epsilon$-domain. The starting point is the joint probability density of the corresponding random matrix theory. In addition…

For a large class of symmetric random matrices with correlated entries, selected from stationary random fields of centered and square integrable variables, we show that the limiting distribution of eigenvalue counting measure always exists…

Pseudo-hermitian matrices are matrices hermitian with respect to an indefinite metric. They can be thought of as the truncation of pseudo-hermitian operators, defined over some Krein space, together with the associated metric, to a finite…

We compare eigenvalue densities of Wigner random matrices whose elements are independent identically distributed (iid) random numbers with a Levy distribution and maximally random matrices with a rotationally invariant measure exhibiting a…

We discuss the limiting spectral density of real symmetric random matrices. Other than in standard random matrix theory the upper diagonal entries are not assumed to be independent, but we will fill them with the entries of a stochastic…

We study the gaps between consecutive singular values of random rectangular matrices. Specifically, if $M$ is an $n \times p$ random matrix with independent and identically distributed entries and $\Sigma$ is a $n \times n$ deterministic…

Recent theoretical studies of chaotic scattering have encounted ensembles of random matrices in which the eigenvalue probability density function contains a one-body factor with an exponent proportional to the number of eigenvalues. Two…

The eigenvalue spacing of a uniformly chosen random finite unipotent matrix in its permutation action on lines is studied. We obtain bounds for the mean number of eigenvalues lying in a fixed arc of the unit circle and offer an approach…

We consider ensembles of real symmetric band matrices with entries drawn from an infinite sequence of exchangeable random variables, as far as the symmetry of the matrices permits. In general the entries of the upper triangular parts of…

In this paper we consider an asymptotic question in the theory of the Gaussian Unitary Ensemble of random matrices. In the bulk scaling limit, the probability that there are no eigenvalues in the interval (0,2s) is given by P_s=det(I-K_s),…

We study statistical properties of the eigenvectors of non-Hermitian random matrices, concentrating on Ginibre's complex Gaussian ensemble, in which the real and imaginary parts of each element of an N x N matrix, J, are independent random…

We study the asymptotic behavior of the eigenvalues of Gaussian perturbations of large Hermitian random matrices for which the limiting eigenvalue density vanishes at a singular interior point or vanishes faster than a square root at a…

We review our recent results on pseudo-hermitian random matrix theory which were hitherto presented in various conferences and talks. (Detailed accounts of our work will appear soon in separate publications.) Following an introduction of…

We consider the random matrix ensemble with an external source \[ \frac{1}{Z_n} e^{-n \Tr({1/2}M^2 -AM)} dM \] defined on $n\times n$ Hermitian matrices, where $A$ is a diagonal matrix with only two eigenvalues $\pm a$ of equal…

We analytically calculate the average value of i-th largest Schmidt coefficient for random pure quantum states. Schmidt coefficients, i.e., eigenvalues of the reduced density matrix, are expressed in the limit of large Hilbert space size…

Recent work of Bornemann has uncovered hitherto hidden integrable structures relating to the asymptotic expansion of quantities at the soft edge of Gaussian and Laguerre random matrix ensembles. These quantities are spacing distributions…

We consider density matrices which are sums of projectors on states spanning irreducible representations of the permutation group of L sites (eigenstates of permutational invariant quantum system with L sites) and construct the reduced…

For random piecewise linear systems T of the interval that are expanding on average we construct explicitly the density functions of absolutely continuous T-invariant measures. In case the random system uses only expanding maps our…

We consider $N\times N$ symmetric or hermitian random matrices with independent, identically distributed entries where the probability distribution for each matrix element is given by a measure $\nu$ with a subexponential decay. We prove…

It is well known that the joint probability density of the eigenvalues of Gaussian ensembles of random matrices may be interpreted as a Coulomb gas. We review these classical results for hermitian and complex random matrices, with special…