[G-Stats Seminar] Marc Arnaudon

Marc Arnaudon

Université de Bordeaux, France

25/05/2022 – h. 11 a.m.

Coupling of Brownian motions with set valued dual processes on Riemannian manifolds; application to perfect simulation

Abstract: In this talk we will motivate and explain the evolution by renormalized stochastic mean curvature flow, of boundaries of relatively compact connected domains in a Riemannian manifold. We will construct coupled Brownian motions inside the moving domains, satisfying a Markov intertwining relation. We will prove that the Brownian motions perform perfect simulation of uniform law, when the domain reaches the whole manifold. We will investigate the example of evolution of discs in spheres, and of symmetric domains in R^2. Skeletons of moving domains will play a major role.

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