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 sufficient conditions for the number rigidity of a large class of point processes in
dimension d= 1 d= 1 and 2, based on the decay of correlations. Number rigidity implies that …

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 …

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 study the mutual regularity properties of Palm measures of point processes, and
establish that a key determining factor for these properties is the rigidity-tolerance behaviour …

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 the convergence of N-particle systems of Brownian particles with logarithmic
interaction potentials onto a system described by the infinite-dimensional stochastic …

We prove the sets of polynomials on configuration spaces are cores of Dirichlet forms
describing interacting Brownian motion in infinite dimensions. Typical examples of these …

We introduce and study a notion of duality for two classes of optimization problems
commonly occurring in probability theory. That is, on an abstract measurable space (Ω, F) …