36 citations · 125 across the 24 of their papers we have counts for
31 papers
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…
Asymptotics for Random Quadratic Transportation Costs
Martin Huesmann, Michael Goldman, Dario Trevisan
We establish the validity of asymptotic limits for the general transportation problem between random i.i.d. points and their common distribution, with respect to the squared Euclid…
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…
Almost sharp rates of convergence for the average cost and displacement in the optimal matching problem
Michael Goldman, Martin Huesmann, Felix Otto
In this note we prove estimates for the average cost in the quadratic optimal transport problem on the two-dimensional flat torus which are optimal up to a double logarithm. We als…
There is no stationary -cyclically monotone Poisson matching in 2D
Martin Huesmann, Francesco Mattesini, Felix Otto
We show that for there is no -cyclically monotone stationary matching of two independent Poisson processes in dimension . The proof combines the -harmonic approxim…
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…