Related papers: Duality in random matrix ensembles for all Beta
In the classical $\beta$-ensembles of random matrix theory, setting $\beta = 2 \alpha/N$ and taking the $N \to \infty$ limit gives a statistical state depending on $\alpha$. Using the loop equations for the classical $\beta$-ensembles, we…
We present a Gaussian ensemble of random cyclic matrices on the real field and study their spectral fluctuations. These cyclic matrices are shown to be pseudo-symmetric with respect to generalized parity. We calculate the joint probability…
Dirichlet integrals and the associated Dirichlet statistical densities are widely used in various areas. Generalizations of Dirichlet integrals and Dirichlet models to matrix-variate cases, when the matrices are real symmetric positive…
We consider random Hermitian matrices made of complex or real $M\times N$ rectangular blocks, where the blocks are drawn from various ensembles. These matrices have $N$ pairs of opposite real nonvanishing eigenvalues, as well as $M-N$ zero…
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…
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 large non-Hermitian real or complex random matrices $X$ with independent, identically distributed centred entries. We prove that their local eigenvalue statistics near the spectral edge, the unit circle, coincide with those of…
We consider two families of non-Hermitian Gaussian random matrices, namely the elliptical Ginibre ensembles of asymmetric N-by-N matrices with Dyson index beta=1 (real elements) and with beta=4 (quaternion-real elements). Both ensembles…
One object of interest in random matrix theory is a family of point ensembles (random point configurations) related to various systems of classical orthogonal polynomials. The paper deals with a one--parametric deformation of these…
The Householder reduction of a member of the anti-symmetric Gaussian unitary ensemble gives an anti-symmetric tridiagonal matrix with all independent elements. The random variables permit the introduction of a positive parameter $\beta$,…
This paper adapts the recently developed rigorous application of the supersymmetric transfer matrix approach for the 1d band matrices to the case of the orthogonal symmetry. We consider $N\times N$ block band matrices consisting of $W\times…
The full spectrum of transfer matrices of the general eight-vertex model on a square lattice is obtained by numerical diagonalization. The eigenvalue spacing distribution and the spectral rigidity are analyzed. In non-integrable regimes we…
Random matrix models based on an integral over supermatrices are proposed as a natural extension of bosonic matrix models. The subtle nature of superspace integration allows these models to have very different properties from the analogous…
We discuss an interesting duality known to occur for certain complex reflection groups, namely the duality groups. Our main construction yields a concrete, representation theoretic realisation of this duality. This allows us to naturally…
Spectral correlations in unitary invariant, non-Gaussian ensembles of large random matrices possessing an eigenvalue gap are studied within the framework of the orthogonal polynomial technique. Both local and global characteristics of…
In this paper we prove some characterizations of the matrix orthogonal polynomials whose derivatives are also orthogonal, which generalize other known ones in the scalar case. In particular, we prove that the corresponding orthogonality…
Gross, Mansour and Tucker introduced the partial-twuality polynomial of a ribbon graph. Chumutov and Vignes-Tourneret posed a problem: it would be interesting to know whether the partial duality polynomial and the related conjectures would…
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…
A remarkable property of Hermitian ensembles is their universal behavior, that is, once properly rescaled the eigenvalue statistics does not depend on particularities of the ensemble. Recently, normal matrix ensembles have attracted…
We compute exact asymptotic results for the probability of the occurrence of large deviations of the largest (smallest) eigenvalue of random matrices belonging to the Gaussian orthogonal, unitary and symplectic ensembles. In particular, we…