In this paper, we investigate the mean field games with $ K $ classes of agents who are
weakly coupled via the empirical measure. The underlying dynamics of the representative …

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

In this paper, we investigate the mean field games of N agents who are weakly coupled via
the empirical measures. The underlying dynamics of the representative agent is assumed to …

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

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 that the tagged particles of infinitely many Brownian particles in R 2 interacting via
a logarithmic (two-dimensional Coulomb) potential with inverse temperature β= 2 are sub …

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 …

Abstract Noncolliding Brownian motion (Dyson's Brownian motion model with parameter β=
2) and noncolliding Bessel processes are determinantal processes; that is, their space–time …

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