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 …

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

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 give a new sufficient condition of the quasi-Gibbs property. This result is a refinement of
one given in a previous paper (Osada (in press)[18]), and will be used in a forthcoming …

We prove tightness and limiting Brownian-Gibbs description for line ensembles of non-
colliding Brownian bridges above a hard wall, which are subject to geometrically growing …

We give a derivation of tagged particle processes from unlabeled interacting Brownian
motions. We give a criteria of the non-explosion property of tagged particle processes. We …

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 …