3 papers
math.PR2026
(Non)-hyperuniformity of perturbed lattices
David Dereudre, Daniela Flimmel, Martin Huesmann +1
We ask whether a stationary lattice in dimension whose points are shifted by identically distributed but possibly dependent perturbations remains hyperuniform. When or…
math.PR2025
The link between hyperuniformity, Coulomb energy, and Wasserstein distance to Lebesgue for two-dimensional point processes
Martin Huesmann, Thomas Leblé
We investigate the interplay between three possible properties of stationary point processes: i) Finite Coulomb energy with short-scale regularization, ii) Finite -Wasserstein t…
math.PR2025
Non-local Wasserstein Geometry, Gradient Flows, and Functional Inequalities for Stationary Point Processes
Martin Huesmann, Hanna Stange
We construct a non-local Benamou-Brenier-type transport distance on the space of stationary point processes and analyse the induced geometry. We show that our metric is a specific…