Related papers: The random normal matrix model: insertion of a poi…

We extend the method of rescaled Ward identities of Ameur-Kang-Makarov to study the distribution of eigenvalues close to a bulk singularity, i.e. a point in the interior of the droplet where the density of the classical equilibrium measure…

We study the characteristic polynomial $p_{n}(x)=\prod_{j=1}^{n}(|z_{j}|-x)$ where the $z_{j}$ are drawn from the Mittag-Leffler ensemble, i.e. a two-dimensional determinantal point process which generalizes the Ginibre point process. We…

We consider a family of random normal matrix models whose eigenvalues tend to occupy lemniscate type droplets as the size of the matrix increases. Under the insertion of a point charge, we derive the scaling limit at the singular boundary…

We show in this paper that after proper scalings, the characteristic polynomial of a random unitary matrix converges almost surely to a random analytic function whose zeros, which are on the real line, form a determinantal point process…

The second author had previously obtained explicit generating functions for moments of characteristic polynomials of permutation matrices (n points). In this paper, we generalize many aspects of this situation. We introduce random shifts of…

Number theorists have studied extensively the connections between the distribution of zeros of the Riemann $\zeta$-function, and of some generalizations, with the statistics of the eigenvalues of large random matrices. It is interesting to…

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 construct a class of random matrix ensembles labelled by a real parameter $\alpha \in (0,1)$, whose eigenvalue density near zero behaves like $|x|^\alpha$. The eigenvalue spacing near zero scales like $1/N^{1/(1+\alpha)}$…

Universality of eigenvalue spacings is one of the basic characteristics of random matrices. We give the precise meaning of universality and discuss the standard universality classes (sine, Airy, Bessel) and their appearance in unitary,…

We consider the logarithm of the characteristic polynomial of random permutation matrices, evaluated on a finite set of different points. The permutations are chosen with respect to the Ewens distribution on the symmetric group. We show…

Let $X_N$ be an $N\ts N$ random symmetric matrix with independent equidistributed entries. If the law $P$ of the entries has a finite second moment, it was shown by Wigner \cite{wigner} that the empirical distribution of the eigenvalues of…

We have discussed earlier the correlation functions of the random variables $\det(\la-X)$ in which $X$ is a random matrix. In particular the moments of the distribution of these random variables are universal functions, when measured in the…

We consider unitary random matrix ensembles Z_{n,s,t}^{-1}e^{-n tr V_{s,t}(M)}dM on the space of Hermitian n x n matrices M, where the confining potential V_{s,t} is such that the limiting mean density of eigenvalues (as n\to\infty and…

We study unitary random matrix ensembles in the critical case where the limiting mean eigenvalue density vanishes quadratically at an interior point of the support. We establish universality of the limits of the eigenvalue correlation…

We study the spectral properties of a class of random matrices where the matrix elements depend exponentially on the distance between uniformly and randomly distributed points. This model arises naturally in various physical contexts, such…

In this article we study in detail a family of random matrix ensembles which are obtained from random permutations matrices (chosen at random according to the Ewens measure of parameter $\theta>0$) by replacing the entries equal to one by…

We study the universal properties of distributions of eigenvalues of random matrices in the large $N$ limit. The distributions fall in universality classes characterized entirely by the support of the spectral density.

We study existence and universality of scaling limits for the eigenvalues of a random normal matrix, in particular at points on the boundary of the spectrum. Our approach uses Ward's equation, which is an identity satisfied by the 1-point…

The eigenspinor approach uses the classical amplitude of the algebraic Lorentz rotation connecting the lab and rest frames to study the relativistic motion of particles. It suggests a simple covariant extension of the common definition of…

We formulate gaussian and circular random-matrix models representing a coupled system consisting of an absorbing and an amplifying resonator, which are mutually related by a generalized time-reversal symmetry. Motivated by optical…