A Benamou-Brenier formula for transport distances between stationary random measures (2402.04842v1)

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.