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A particle model for Wasserstein type diffusion

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If you have a question about this talk, please contact Perla Sousi.

The discussion will be devoted to a family of interacting particles on the real line which have a connection with the geometry of Wasserstein space of probability measures. We will consider a physical improvement of a classical Arratia flow, but now particles can split up and they transfer a mass that influences their motion. The particle system can be also interpreted as an infinite dimensional version of sticky reflecting dynamics on a simplicial complex. The model appears as a martingale solution to an infinite dimensional SDE with discontinuous coefficients. In the talk, we are going to consider a reversible case, where the construction is based on a new family of measures on the set of real non-decreasing functions as reference measures for naturally associated Dirichlet forms. In this case, the intrinsic metric leads to a Varadhan formula for the short time asymptotics with the Wasserstein metric for the associated measure valued diffusion. The talk is based on joint work with Max von Renesse.

This talk is part of the Probability series.

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