Asymptotics of spectral gaps on loop spaces over a class of Riemannian   manifolds
  We prove the existence of spectral gaps of Ornstein-Uhlenbeck operators on loop spaces over a class of Riemannian manifolds which include hyperbolic spaces. This is an alternative proof and an extension of a result in Chen-Li-Wu in J. Funct. Anal. 259 (2010), 1421-1442. Further, we study the asymptotic behavior of the spectral gap. 
Shigeki Aida
math.PR