# Isometric rigidity of Wasserstein spaces: the graph metric case

@inproceedings{Kiss2022IsometricRO, title={Isometric rigidity of Wasserstein spaces: the graph metric case}, author={Gergely Kiss and Tam'as Titkos}, year={2022} }

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

## 3 Citations

### Isometric rigidity of Wasserstein tori and spheres

- MathematicsMathematika
- 2022

We prove isometric rigidity for p‐Wasserstein spaces over finite‐dimensional tori and spheres for all p. We present a unified approach to proving rigidity that relies on the robust method of…

### Quantum Wasserstein isometries on the qubit state space

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### The isometry group of Wasserstein spaces: the Hilbertian case

- MathematicsJournal of the London Mathematical Society
- 2022

Motivated by Kloeckner's result on the isometry group of the quadratic Wasserstein space W2(Rn)$\mathcal {W}_2(\mathbb {R}^n)$ , we describe the isometry group Isom(Wp(E))$\mathrm{Isom}(\mathcal…

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