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.
"Remarks on spectral gaps on the Riemannian path space." Electron. Commun. Probab. 22 1 - 13, 2017. https://doi.org/10.1214/17-ECP51