We review the development of random-matrix theory (RMT) during the last fifteen years. We
emphasize both the theoretical aspects, and the application of the theory to a number of …

During the last few years quantum graphs have become a paradigm of quantum chaos with
applications from spectral statistics to chaotic scattering and wavefunction statistics. In the …

Normal-conducting mesoscopic systems in contact with a superconductor are classified by
the symmetry operations of time reversal and rotation of the electron's spin. Four symmetry …

A new approach is presented for analyzing random uncertainties in dynamical systems. This
approach consists of modeling random uncertainties by a nonparametric model allowing …

We consider random non-hermitian matrices in the large-N limit. The power of analytic
function theory cannot be brought to bear directly to analyze non-hermitian random matrices …

We consider polynomials that are orthogonal on [− 1, 1] with respect to a modified Jacobi
weight (1− x) α (1+ x) βh (x), with α, β>− 1 and h real analytic and strictly positive on [− 1, 1] …

Let ξ be a real-valued random variable of mean zero and variance 1. Let M n (ξ) denote the
n× n random matrix whose entries are iid copies of ξ and σ n (M n (ξ)) denote the least …

We investigate one-dimensional (1D) discrete-time quantum walks (QWs) with spatially or
temporally random defects as a consequence of interactions with random environments. We …

We study the eigenvalues of the covariance matrix 1/n M∗ M of a large rectangular matrix
M= M n, p=(ζ ij) 1≤ i≤ p; 1≤ j≤ n whose entries are iid random variables of mean zero …

We apply the recently introduced method of hermitization to study in the large N limit non-
hermitian random matrices that are drawn from a large class of circularly symmetric non …