Isometric rigidity of Wasserstein spaces: The graph metric case

Kiss, Gergely; Titkos, Tamás

doi:10.1090/proc/15977

Isometric rigidity of Wasserstein spaces: The graph metric case
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by Gergely Kiss and Tamás Titkos PDF

Proc. Amer. Math. Soc. 150 (2022), 4083-4097 Request permission

Abstract:

The aim of this paper is to prove that the $p$-Wasserstein space $\mathcal {W}_p(X)$ is isometrically rigid for all $p\geq 1$ whenever $X$ is a countable graph metric space. As a consequence, we obtain that for every countable group ${H}$ and any $p\geq 1$ there exists a $p$-Wasserstein space whose isometry group is isomorphic to ${H}$.

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