English

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}
}