The University of Arizona: The Wasserstein geometry of random measures through superposition principles
In this talk, I will introduce the space of random measures $\mathcal{P}_p(\mathcal{P}_p(X))$, endowed with the Wasserstein-on-Wasserstein metric, where $(X, d)$ is a complete separable metric space. In this setting, we prove a metric superposition principle, that will allow us to recover important geometric features of the space. When $X$ is $\mathbb{R}^d$, we will se also...