Spectral gap on Riemannian path space over static and evolving manifolds
Probability
2016-11-08 v1
Abstract
In this article, we continue the discussion of Fang-Wu (2015) to estimate the spectral gap of the Ornstein-Uhlenbeck operator on path space over a Riemannian manifold of pinched Ricci curvature. Along with explicit estimates we study the short-time asymptotics of the spectral gap. The results are then extended to the path space of Riemannian manifolds evolving under a geometric flow. Our paper is strongly motivated by Naber's recent work (2015) on characterizing bounded Ricci curvature through stochastic analysis on path space.
Cite
@article{arxiv.1611.02165,
title = {Spectral gap on Riemannian path space over static and evolving manifolds},
author = {Li-Juan Cheng and Anton Thalmaier},
journal= {arXiv preprint arXiv:1611.02165},
year = {2016}
}