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