Electronic Communications in Probability

Remarks on spectral gaps on the Riemannian path space

Shizan Fang and Bo Wu

Full-text: Open access

Abstract

In this paper, we will give some remarks on links between the spectral gap of the Ornstein-Uhlenbeck operator on the Riemannian path space with lower and upper bounds of the Ricci curvature on the base manifold; this work was motivated by a recent work of A. Naber on the characterization of the bound of the Ricci curvature by analysis of path spaces.

Article information

Source
Electron. Commun. Probab., Volume 22 (2017), paper no. 19, 13 pp.

Dates
Received: 10 March 2016
Accepted: 27 February 2017
First available in Project Euclid: 14 March 2017

Permanent link to this document
https://projecteuclid.org/euclid.ecp/1489457081

Digital Object Identifier
doi:10.1214/17-ECP51

Mathematical Reviews number (MathSciNet)
MR3627008

Zentralblatt MATH identifier
1365.58019

Subjects
Primary: 58J60: Relations with special manifold structures (Riemannian, Finsler, etc.) 60H07: Stochastic calculus of variations and the Malliavin calculus 60J60: Diffusion processes [See also 58J65]

Keywords
damped gradient martingale representation Ricci curvature spectral gap small time behaviour

Rights
Creative Commons Attribution 4.0 International License.

Citation

Fang, Shizan; Wu, Bo. Remarks on spectral gaps on the Riemannian path space. Electron. Commun. Probab. 22 (2017), paper no. 19, 13 pp. doi:10.1214/17-ECP51. https://projecteuclid.org/euclid.ecp/1489457081


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