This book gives a comprehensive and self-contained introduction to the theory of symmetric
Markov processes and symmetric quasi-regular Dirichlet forms. In a detailed and accessible …

We introduce certain classes of random point fields, including fermion and boson point
processes, which are associated with Fredholm determinants of certain integral operators …

In this paper foundations are presented to a new systematic approach to analysis and
geometry for an important class of infinite dimensional manifolds, namely, configuration …

Using a natural “Riemannian geometry-like” structure on the configuration spaceΓover R d,
we prove that for a large class of potentialsφthe corresponding canonical Gibbs measures …

We investigate the construction of diffusions consisting of infinitely numerous Brownian
particles moving in R^d and interacting via logarithmic functions (two-dimensional Coulomb …

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

The constuction of models of non-relativistic quantum fields via current algebra
representations is presented using a natural differential geometry of the configuration space …

Γx:=[γ CX Iγ ΠK is a finite set for every compact K c X] equipped with the vague topology via
the identification γ= ΣxeYεχ In t3! a nat~ ural" differential geometry" was introduced on Γx via …