Spectral gap on Riemannian path space over static and evolving manifolds

2016/11/07 by Cheng, Li-Juan, Thalmaier, Anton
#53C44 #58J65 #60J60 #FOS: Mathematics #Probability (math.PR)

paper · doi:10.48550/arxiv.1611.02165

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.

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