Remarks on spectral gaps on the Riemannian path space

Shizan Fang (1) , Bo Wu (2)

1 IMB - Institut de Mathématiques de Bourgogne [Dijon]
2 Department of Mathematics, Fudan University

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.

Mots clés: AMS subject Classification: 58J60; 60H07; 60J60 Keyword: Damped gradient; Martingale representation; Ricci curvature; spectral gap; small time behaviour

Domaines: Probabilités [math.PR]

Shizan Fang, Bo Wu. Remarks on spectral gaps on the Riemannian path space. 2015. ⟨hal-01192833⟩