Electronic Communications in Probability

Remarks on spectral gaps on the Riemannian path space

Shizan Fang and Bo Wu

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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

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

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

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Zentralblatt MATH identifier

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]

damped gradient martingale representation Ricci curvature spectral gap small time behaviour

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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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