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Optimal transport for stationary point processes

  • Matthias Erbar (Universität Bielefeld)
E1 05 (Leibniz-Saal)

Abstract

We develop a theory of optimal transport for stationary random measures with a particular focus on stationary point processes. This provides us with a notion of geodesic distance between distributions of stationary random measures and induces a natural displacement interpolation between them. In the setting of stationary point processes we leverage this transport distance to give a geometric interpretation for the evolution of infinite particle systems with stationary distribution. Namely, we characterise the evolution of infinitely many Brownian motions as the gradient flow of the specific relative entropy w.r.t.~the Poisson process. Further, we establish displacement convexity of the specific relative entropy along optimal interpolations of point processes. This is joint work with Martin Huesmann, Jonas Jalowy and Bastian Müller

Katja Heid

MPI for Mathematics in the Sciences Contact via Mail

Upcoming Events of this Seminar

  • Tuesday, 04.06.24 tba with Vadim Gorin
  • Tuesday, 11.06.24 tba
  • Tuesday, 25.06.24 tba with Paul Dario
  • Tuesday, 25.06.24 tba with Julian Fischer
  • Tuesday, 16.07.24 tba with Michael Loss
  • Tuesday, 20.08.24 tba with Tomasz Komorowski
  • Tuesday, 03.12.24 tba with Patricia Gonçalves