Optimal transport for stationary point processes

Description

Optimal transport by now has found manifold applications in various areas of mathematics, in particular it has turned into a powerful tool in the analysis of stochastic processes, particle dynamics, and the associated evolution equations, mostly however in a finite-dimensional setting. The goal of this project is to develop a counterpart to this theory in the framework of stationary point processes or more general random (infinite) measures and to employ these novel tools e.g. in the analysis of infinite particle dynamics or to attack questions for particular point process models of interest.

Preprints/Publications

Brian C. Hall, Ching-Wei Ho, Jonas Jalowy, Zakhar Kabluchko: Zeros of random polynomials undergoing the heat flow (08/2023)

Jonas Jalowy, Zakhar Kabluchko, Matthias Löwe, Alexander Marynych: When does the chaos in the Curie-Weiss model stop to propagate? (07/2023)

Matthias Erbar, Martin Huesmann, Jonas Jalowy, Bastian Müller: Optimal transport of stationary point processes: Metric structure, gradient flow and convexity of the specific entropy (04/2023)

Brian Hall, Ching-Wei Ho, Jonas Jalowy, Zakhar Kabluchko: The heat flow, GAF, and SL(2;R) (04/2023)

Martin Huesmann, Bastian Müller: Transportation of random measures not charging small sets (03/2023)

Jonas Jalowy: The Wasserstein distance to the Circular Law (11/2021)

Members

  • member's portrait

    Prof. Dr. Matthias Erbar

    Universität Bielefeld
    Principal Investigator
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    Prof. Dr. Martin Huesmann

    Westfälische Wilhelms-Universität Münster
    Principal Investigator
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    Dr. Jonas Jalowy

    Westfälische Wilhelms-Universität Münster
    Associated Scientist
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    M. Sc. Bastian Müller

    Westfälische Wilhelms-Universität Münster
    Associated Scientist

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