## Electronic Communications in Probability

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

### Remarks on spectral gaps on the Riemannian path space

Shizan Fang and Bo Wu

#### 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