Diffusion bridges and log-derivatives of the heat kernel in small time

Robert Neel (Lehigh University)

Mercredi 7 septembre, 11:00, salle Coriolis (Galois).

Abstract. Consider a sub-Riemannian manifold with a sub-Laplacian and associated heat kernel and diffusion process. For two fixed points, we show that the small-time limit of the bridge process between the points, which is the law of large numbers in this context, is determined by the geometry of the minimal geodesics between the points. Moreover, this limiting distribution plays a fundamental role in the small-time behavior of the logarithmic-derivatives of the heat kernel. The method is fundamentally local and remains valid on incomplete manifolds under appropriate conditions on the distance to infinity, and this leads to new results even in the Riemannian case.

This talk is based on joint work with Ludovic Sacchelli.