Abstract
In this paper, we give a simple proof of log-Sobolev inequalities on an infinite volume path space C (ℝ, ℝd) with Gibbs measures. We introduce a parabolic stochastic partial differential equation which is reversible with respect to the Gibbs measures. In the proof, the gradient estimate for the diffusion semigroup which is derived from the stochastic flow plays a central role.
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