A simple proof of log-Sobolev inequalities on a path space with Gibbs measures

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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.

Original languageEnglish
Pages (from-to)321-329
Number of pages9
JournalInfinite Dimensional Analysis, Quantum Probability and Related Topics
Volume9
Issue number2
DOIs
Publication statusPublished - 2006 Jun 1

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Keywords

  • Gibbs measure
  • Gradient estimate
  • Log-Sobolev inequality
  • SPDE

ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Statistics and Probability
  • Mathematical Physics
  • Applied Mathematics

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