THE DIRICHLET-FERGUSON DIFFUSION ON THE SPACE OF PROBABILITY MEASURES OVER A CLOSED RIEMANNIAN MANIFOLD

• 成果类型: Article
• 署名作者: Dello Schiavo, Lorenzo
• 署名单位: Institute of Science & Technology - Austria
• 刊物名称: ANNALS OF PROBABILITY
• ISSN/ISSBN: 0091-1798
• DOI: 10.1214/21-AOP1541
• 发表日期: 2022
• 页码: 591-648
• 关键词: fleming-viot processes; quasi-invariance; entropic measure; CONVERGENCE; Operators; forms

摘要

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 with the Dirichlet form defined by integration of the Wasserstein gradient w.r.t. the Dirichlet-Ferguson measure, and is the counterpart on multidimensional base spaces to the modified massive Arratia flow over the unit interval described in V. Konarovskyi and M.-K. von Renesse (Comm. Pure Appl. Math. 72 (2019) 764-800). Together with two different constructions of the process, we discuss its ergodicity, invariant sets, finite-dimensional approximations, and Varadhan short-time asymptotics.