This book contains an introductory and comprehensive account of the theory of (symmetric)
Dirichlet forms. Moreover this analytic theory is unified with the probabilistic potential theory …

We study a physical system of N interacting particles in R^d, d\geq1, subject to pair
repulsion and confined by an external field. We establish a large deviations principle for …

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 solve infinite-dimensional stochastic differential equations (ISDEs) describing an infinite
number of Brownian particles interacting via two-dimensional Coulomb potentials. The …

The Airy $ _\beta $ line ensemble is an infinite sequence of random curves. It is a natural
extension of the Tracy-Widom $ _\beta $ distributions, and is expected to be the universal …

We consider particle systems (also known as point processes) on the line and in the plane
and are particularly interested in “hole” events, when there are no particles in a large disk (or …

We construct a four-parameter family of Markov processes on infinite Gelfand–Tsetlin
schemes that preserve the class of central (Gibbs) measures. Any process in the family …

In this paper we show the strong existence and the pathwise uniqueness of an infinite-
dimensional stochastic differential equation (SDE) corresponding to the bulk limit of Dyson's …

We construct a canonical differential structure on the configuration space $\Upsilon $ over a
singular base space $ X $ and with a general invariant measure $\mu $ on $\Upsilon $. We …

Dyson's model is a one-dimensional system of Brownian motions with long-range repulsive
forces acting between any pair of particles with strength proportional to the inverse of …