Wasserstein diffusion on multidimensional spaces
Abstract
Given any closed Riemannian manifold M, we construct a stochastic perturbation of the heat flow as a continuous Markov process on the space P(M) of probability measures on M, that is: (1) reversible w.r.t. the entropic measure Pβ on P(M), heuristically given as dPβ(μ)=1 Ze−βEnt(μ|m)dP∗(μ); (2) associated with a regular Dirichlet form with carré du champ derived from the Wasserstein gradient in the sense of Otto calculus EW(f)=lim infg→f 1 2∫P(M)‖∇Wg‖2(μ)dPβ(μ); (3) nondegenerate, at least in the case of the n-sphere and the n-torus. And yet it moves. Galileo Galilei, 1633
Fields of Study & Subjects
Geometric Analysis and Curvature Flows
Stochastic processes and statistical mechanics
Markov Chains and Monte Carlo Methods
Publication details
- Journal / source
- The Annals of Probability
- Volume
- 54
- Issue
- 2
- Pages
- 610–643
- Publication date
- 26 February 2026
- Language
- EN