Logarithmic sobolev inequalities on path spaces over riemannian manifolds

Elton P. Hsu*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

34 Scopus citations

Abstract

Let Wo(M) be the space of paths of unit time length on a connected, complete Riemannian manifold M such that γ(0) = o, a fixed point on M, and v the Wiener measure on Wo(M) (the law of Brownian motion on M starting at o). If the Ricci curvature is bounded by c, then the following logarithmic Sobolev inequality holds: ∫Wo(M) F2 log |F|dv ≤ e3c∥DF∥2 + ∥F∥2 log ∥F∥.

Original languageEnglish (US)
Pages (from-to)9-16
Number of pages8
JournalCommunications in Mathematical Physics
Volume189
Issue number1
DOIs
StatePublished - Jan 1 1997

ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Mathematical Physics

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