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Convergence of Brownian motions on RCD*(K,N) spaces
Kohei Suzuki · 2015-09-07 · via math.PR updates on arXiv.org

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.

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