Log-Sobolev inequalities on the horizontal path space of a totally geodesic foliation
Probability
2015-03-30 v1 Differential Geometry
Abstract
We develop a Malliavin calculus on the horizontal path space of a totally geodesic Riemannian foliation. As a first application, under suitable assumptions, we prove a log-Sobolev inequality for a natural one-parameter family of infinite-dimensional Ornstein-Uhlenbeck type operators. As a second application, we obtain concentration and tail estimates for the horizontal Brownian motion of the foliation.
Keywords
Cite
@article{arxiv.1503.08180,
title = {Log-Sobolev inequalities on the horizontal path space of a totally geodesic foliation},
author = {Fabrice Baudoin and Qi Feng},
journal= {arXiv preprint arXiv:1503.08180},
year = {2015}
}