Convergence of Brownian motions on RCD(K,infty) spaces

Abstract

Suppose that metric measure spaces X_n=(X_n, d_n, m_n) satisfy RCD(K,infty) conditions with m_n(X_n)=1. Then the measured Gromov convergence (introduced by Gigili-Mondino-Savare '13) of X_n is equivalent to the weak convergence of the laws of Brownian motions on X_n with initial distributions m_n.

Withdrawn because the content of this paper has been fully included in my new manuscript arXiv:1703.07234

References in corpus (3)

• Semiconcave functions in Alexandrov's geometry
• On the Equivalence of the Entropic Curvature-Dimension Condition and Bochner's Inequality on Metric Measure Spaces
• Convergence of continuous stochastic processes on compact metric spaces converging in the Lipschitz distance

Cited by in corpus (1)

• Scaling limits of stochastic processes associated with resistance forms