We survey a number of models from physics, statistical mechanics, probability theory and
combinatorics, which are each described in terms of an orthogonal polynomial ensemble …

We continue the study of the Hermitian random matrix ensemble with external source where
A has two distinct eigenvalues±a of equal multiplicity. This model exhibits a phase transition …

Relations between quantum integrable models solvable by the quantum inverse scattering
method and some aspects of enumerative combinatorics and partition theory are discussed …

As an extension of the theory of Dyson's Brownian motion models for the standard Gaussian
random-matrix ensembles, we report a systematic study of Hermitian matrix-valued …

A system of one-dimensional Brownian motions (BMs) conditioned never to collide with
each other is realized as (i) Dyson's BM model, which is a process of eigenvalues of …

This book is based on my graduate-course lectures given at the Graduate School of
Mathematics of the University of Tokyo in October 2008 (at the invitation of T. Funaki and M …

We study a system of N nonintersecting (1+ 1)-dimensional fluctuating elastic interfaces
(“vicious bridges”) at thermal equilibrium, each subject to periodic boundary condition in the …

The eigenvalue probability density function (PDF) for the Gaussian unitary ensemble has a
well-known analogy with the Boltzmann factor for a classical log-gas with pair potential− log …

A Bernoulli trial describing the escape behavior of a lamb to a safe haven in pursuit by a lion
is studied under restarts. The process ends in two ways: either the lamb makes it to the safe …

We construct the conditional version of k independent and identically distributed random
walks on R given that they stay in strict order at all times. This is a generalisation of so-called …