Convergence of Brownian motions on RCD*(K,N) spaces

Abstract

Suppose that a sequence of metric measure spaces X_n=(X_n, d_n, m_n) satisfies RCD*(K,N) with Diam(X_n) <D and m_n(X_n)=1. Then Sturm's D-convergence of X_n is equivalent to the weak convergence of the laws of Brownian motions on X_n.

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