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Gap metrics for stationary point processes and quantitative convexity of the free energy
Martin Huesmann, Bastian Müller
In this article, we are interested in convexity properties of the free energy for stationary point processes on w.r.t.\ a new geometry inspired by optimal transport. We…
A Benamou-Brenier formula for transport distances between stationary random measures
Martin Huesmann, Bastian Müller
We derive a Benamou-Brenier type dynamical formulation for the Wasserstein metric between stationary random measures recently introduced in [EHJM23]. A key step is a…
Optimal transport of stationary point processes: Metric structure, gradient flow and convexity of the specific entropy
Matthias Erbar, Martin Huesmann, Jonas Jalowy +1
We develop a theory of optimal transport for stationary random measures with a focus on stationary point processes and construct a family of distances on the set of stationary rand…
Transportation of random measures not charging small sets
Martin Huesmann, Bastian Müller
Let be a pair of jointly stationary, ergodic random measures of equal finite intensity. A balancing allocation is a translation-invariant (equivariant) map $T:\mathbb{R}^d\…