Alessandro Pinzi

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math.FA2025

Nested superposition principle for random measures and the geometry of the Wasserstein on Wasserstein space

Alessandro Pinzi, Giuseppe Savaré

We study the geometric structure of the space of random measures $P_{p} (P_{p} (X))$ , endowed with the Wasserstein on Wasserstein metric, where $(X, d)$ is a complete…

math.FA2025

Totally convex functions, $L^{2}$ -Optimal transport for laws of random measures, and solution to the Monge problem

Alessandro Pinzi, Giuseppe Savaré

We study the Optimal Transport problem for laws of random measures in the Kantorovich-Wasserstein space $P_{2} (P_{2} (H))$ , associated with a Hilbert space…

Nested superposition principle for random measures and the geometry of the Wasserstein on Wasserstein space

Totally convex functions, L2-Optimal transport for laws of random measures, and solution to the Monge problem

Totally convex functions, $L^{2}$ -Optimal transport for laws of random measures, and solution to the Monge problem