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 et al. . Further, we study the asymptotic behavior of the spectral gap.
- Logarithmic Sobolev inequality
- Loop space
- Semi-classical limit
- Spectral gap
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