Barycentres convexes et approximations des martingales continues dans les variétés
Barycentres et martingales sur une variété
Brownian motion and random walks on manifolds
We develop a procedure that allows us to “descretise” the Brownian motion on a Riemannian manifold. We construct thus a random walk that is a good approximation of the Brownian motion.
Brownian motion and stereographic projection
Brownian motion and transient groups
In this paper I consider a covering of a Riemannian manifold . I prove that Green’s function exists on if any and only if the symmetric translation invariant random walks on the covering group are transient (under the assumption that is compact).
Brownian motion, excursions, and matrix factors
Brownian motion on a surface of negative curvature
Brownian motion on compact manifolds: cover time and late points.
Brownian motion with respect to time-changing riemannian metrics, applications to Ricci flow
We generalize brownian motion on a riemannian manifold to the case of a family of metrics which depends on time. Such questions are natural for equations like the heat equation with respect to time dependent laplacians (inhomogeneous diffusions). In this paper we are in particular interested in the Ricci flow which provides an intrinsic family of time dependent metrics. We give a notion of parallel transport along this brownian motion, and establish a generalization of the Dohrn–Guerra or damped...
Brownian motions in the diffeomorphism group I