Random matrix theory is a wide and growing field with a variety of concepts, results, and
techniques and a vast range of applications in mathematics and the related sciences. The …

There are a number of intriguing connections between Painlevé equations and orthogonal
polynomials, and this book is one of the first to provide an introduction to these. Researchers …

This paper is concerned with Hermite-Padé rational approximants of analytic functions and
their connection with multiple orthogonal polynomial ensembles of random matrices. Results …

We prove universality at the edge of the spectrum for unitary (β= 2), orthogonal (β= 1), and
symplectic (β= 4) ensembles of random matrices in the scaling limit for a class of weights w …

We construct approximate transport maps for non-critical β β-matrix models, that is, maps so
that the push forward of a non-critical β β-matrix model with a given potential is a non-critical …

We prove a central limit theorem for the linear statistics of one-dimensional log-gases, or β-
ensembles. We use a method based on a change of variables which allows to treat fairly …

We consider the double scaling limit in the random matrix ensemble with an external source
1 Z_n e^-n Tr (1\over 2 M^ 2-AM) dM defined on n× n Hermitian matrices, where A is a …

A bstract We take a step towards the non-perturbative description of a two-dimensional
dilaton-gravity theory which has a vanishing cosmological constant and contains black …

We construct a Hermitian random matrix model that provides a stable nonperturbative
completion of Cangemi-Jackiw (CJ) gravity, a two-dimensional theory of flat spacetimes. The …

We study unitary random matrix ensembles of the form Z_n,N^-1|\detM|^2αe^-NTrV(M)dM,
where α>-1/2 and V is such that the limiting mean eigenvalue density for n, N→∞ and n/N→ …