Seminar für Stochastische Analysis – Matthias Erbar

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Matthias Erbar Title: Optimal transport and gradient flows for point processes Abstract I will describe a theory of optimal transport for stationary random measures with a focus on stationary point processes. We consider two types of distances on stationary probability measures on the configuration space geared towards different dynamics of point configurations. The first one is based on continuous displacement of points and leads to a two layer optimal transport problem with a probabilistic constraint. It gives rise to a natural notion of displacement interpolation between point processes an…