Wasserstein geometry and Ricci curvature bounds for Poisson spaces (Q6603926)

The authors construct a Riemannian structure on the space of Poisson point processes, where the intrinsic distance \(W\) corresponds to the Benamou-Brenier variational formula, the closure of the domain of the relative entropy is a complete geodesic space, and the Ricci curvature is bounded below by \(1\). Moreover, the Ornstein-Uhlenbeck semigroup is associated with the gradient flow of the relative entropy, and the HWI inequality holds true.