A Benamou-Brenier formula for transport distances between stationary random measures

Abstract

We derive a Benamou-Brenier type dynamical formulation for the Wasserstein metric ${\mathsf{W}}_p$ between stationary random measures recently introduced in [EHJM23]. A key step is a reformulation of the metric ${\mathsf{W}}_p$ using Palm probabilities.

comments welcome