Ismaël Bailleul

DataSig

Kinetic Brownian motion in the diffeomorphism group of a closed Riemannian manifold

<h2>Abstract</h2><p>In its simplest instance, kinetic Brownian in Rᵈ is a C¹ random path (mₜ, vₜ) with unit velocity vₜ a Brownian motion on the unit sphere run at speed a &gt; 0. Properly time rescaled as a function of the parameter a, its position process converges to a Brownian motion in Rᵈ as a tends to infinity. On the other side the motion converges to the straight line motion (= geodesic motion) when a goes to 0. Kinetic Brownian motion provides thus an interpolation between geodesic and Brownian flows in this setting. Think now about changing Rᵈ for the diffeomorphism group of a fluid domain, with a velocity vector now a vector field on the domain. I will explain how one can prove in this setting an interpolation result similar to the previous one, giving an interpolation between Euler’s equations of incompressible flows and a Brownian-like flow on the diffeomorphism group.</p><h2>Our speaker</h2><p>Ismaël Bailleul is an associate professor at the Université de Rennes.</p><p><a href="https://perso.univ-rennes1.fr/ismael.bailleul/" target="_blank" data-msys-clicktrack="0" rel="nofollow noopener noreferrer">Read more</a></p>

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Ismaël Bailleul

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