This book provides the reader with the principal concepts and results related to differential
properties of measures on infinite dimensional spaces. In the finite dimensional case such …

We construct a new random probability measure on the circle and on the unit interval which
in both cases has a Gibbs structure with the relative entropy functional as Hamiltonian. It …

We construct a recurrent diffusion process with values in the space of probability measures
over an arbitrary closed Riemannian manifold of dimension d≥ 2. The process is associated …

In this paper, we consider homogeneous normalized random measures with independent
increments (hNRMI), a class of nonparametric priors recently introduced in the literature …

We construct a system of interacting two-sided Bessel processes on the unit interval and
show that the associated empirical measure process converges to the Wasserstein diffusion …

We consider the infinite-dimensional Lie group G which is the semidirect product of the
group of compactly supported diffeomorphisms of a Riemannian manifold X and the …

We construct the entropic measure P^ β on compact manifolds of any dimension. It is
defined as the push forward of the Dirichlet process (a random probability measure, well …

Abstract The Wasserstein space P (M) on an Euclidean or Riemannian space M–ie the
space of probability measures on M equipped with the L 2-Wasserstein distance d W–offers …

Given any closed Riemannian manifold $ M $, we construct a reversible diffusion process on
the space ${\mathcal P}(M) $ of probability measures on $ M $ that is (i) reversible wrt~ the …

In this study, we investigate a recently introduced class of non‐parametric priors, termed
generalized Dirichlet process priors. Such priors induce (exchangeable random) partitions …