Log-Sobolev inequalities on the horizontal path space of a totally geodesic foliation

Fabrice Baudoin; Qi Feng

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arXiv · 1503.08180

Log-Sobolev inequalities on the horizontal path space of a totally geodesic foliation

Fabrice Baudoin·Qi Feng

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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.

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BibTeX RIS

Fabrice Baudoin, Qi Feng. 2015-03-27. Log-Sobolev inequalities on the horizontal path space of a totally geodesic foliation. https://arxiv.org/abs/1503.08180

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