分野別セミナー

In its simplest instance, kinetic Brownian motion is a one parameter class of $C^1$ random path in $R^d$, run at unit speed, and whose velocity is a Brownian motion on the unit sphere, run at speed a\geq 0; this is the parameter. Propertly time-rescaled, it provides an interpolation between a straight motion (a=0) and Brownian motion (a->\infty). A similar interpolation phenomenon happens for this class of random motions when they takes values in a finite dimensional Riemannian manifold. The family interpolates between geodesic and Brownian flows. What happens of this phenomenon when the manifold is the infinite dimensional group of diffeomorphisms of a compact domain? Geodesics are then solutions to Euler's equations for hydrodynamics and kinetic Brownian motion an intrinsic, geometric, random perturbation of these equations. Joint work with J. Angst & P. Perruchaud.