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 …

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 …

We present general theorems solving the long-standing problem of the existence and
pathwise uniqueness of strong solutions of infinite-dimensional stochastic differential …

We prove tail triviality of determinantal point processes μ μ on continuous spaces. Tail
triviality has been proved for such processes only on discrete spaces, and hence we have …

We develop a unifying theory for four different objects:(1) infinite systems of interacting
massive particles;(2) solutions to the Dean-Kawasaki equation with singular drift and space …

Abstract The Airy\(_ {\beta}\) random point fields (\(\beta= 1, 2, 4\)) are random point fields
emerging as the soft-edge scaling limits of eigenvalues of Gaussian random matrices. We …

We solve the infinite-dimensional stochastic differential equations (ISDEs) describing an
infinite number of Brownian particles in R+ interacting through the two-dimensional …

The Thoma cone is an infinite-dimensional locally compact space, which is closely related to
the space of extremal characters of the infinite symmetric group S_∞. In another context, the …