Spectral gap on Riemannian path space over static and evolving manifolds |
| |
Authors: | Li-Juan Cheng Anton Thalmaier |
| |
Institution: | 1. Mathematics Research Unit, FSTC, University of Luxembourg, Campus Belval – Maison du Nombre, 4364 Esch-sur-Alzette, Luxembourg;2. Department of Applied Mathematics, Zhejiang University of Technology, Hangzhou 310023, People''s Republic of China |
| |
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. |
| |
Keywords: | 60J60 58J65 53C44 Spectral gap Malliavin Calculus Ornstein–Uhlenbeck operator Geometric flow |
本文献已被 ScienceDirect 等数据库收录! |