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Main Authors: Trevisan, Dario, Wang, Feng-Yu, Zhu, Jie-Xiang
Format: Preprint
Published: 2024
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Online Access:https://arxiv.org/abs/2410.21981
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author Trevisan, Dario
Wang, Feng-Yu
Zhu, Jie-Xiang
author_facet Trevisan, Dario
Wang, Feng-Yu
Zhu, Jie-Xiang
contents We identify the leading term in the asymptotics of the quadratic Wasserstein distance between the invariant measure and empirical measures for diffusion processes on closed weighted four-dimensional Riemannian manifolds. Unlike results in lower dimensions, our analysis shows that this term depends solely on the Riemannian volume of the manifold, remaining unaffected by the potential and vector field in the diffusion generator.
format Preprint
id arxiv_https___arxiv_org_abs_2410_21981
institution arXiv
publishDate 2024
record_format arxiv
spellingShingle Wasserstein asymptotics for empirical measures of diffusions on four dimensional closed manifolds
Trevisan, Dario
Wang, Feng-Yu
Zhu, Jie-Xiang
Probability
49Q22, 60B1
We identify the leading term in the asymptotics of the quadratic Wasserstein distance between the invariant measure and empirical measures for diffusion processes on closed weighted four-dimensional Riemannian manifolds. Unlike results in lower dimensions, our analysis shows that this term depends solely on the Riemannian volume of the manifold, remaining unaffected by the potential and vector field in the diffusion generator.
title Wasserstein asymptotics for empirical measures of diffusions on four dimensional closed manifolds
topic Probability
49Q22, 60B1
url https://arxiv.org/abs/2410.21981