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Ouvrages Année : 2022

On the evolution by duality of domains on manifolds

Résumé

On a manifold, consider an elliptic diffusion X admitting an invariant measure μ. The goal of this paper is to introduce and investigate the first properties of stochastic domain evolutions (Dt)t∈[0,τ] which are intertwining dual processes for X (where τ is an appropriate positive stopping time before the potential emergence of singularities). They provide an extension of Pitman’s theorem, as it turns out that (μ(Dt))t∈[0,τ] is a Bessel-3 process, up to a natural time-change. When X is a Brownian motion on a Riemannian manifold, the dual domain-valued process is a stochastic modification of the mean curvature flow to which is added an isoperimetric ratio drift to prevent it from collapsing into singletons.
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Dates et versions

hal-03671574 , version 1 (18-05-2022)

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Abdoulaye Koléhè Coulibaly-Pasquier, Laurent Miclo. On the evolution by duality of domains on manifolds. Société mathématique de France, 171, 110 p., 2022, 978-2-85629-935-7. ⟨10.24033/msmf.479⟩. ⟨hal-03671574⟩

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