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

Research output: Contribution to journalArticle

1 Citation (Scopus)

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
Externally publishedYes

Fingerprint

Log-Sobolev Inequality
Path Space
Gibbs Measure
Partial differential equations
Diffusion Semigroup
Stochastic Flow
Gradient Estimate
Stochastic Partial Differential Equations
Parabolic Partial Differential Equations
partial differential equations
gradients
estimates

Keywords

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

ASJC Scopus subject areas

  • Mathematics(all)
  • Applied Mathematics
  • Statistics and Probability
  • Statistical and Nonlinear Physics
  • Mathematical Physics

Cite this

@article{38f181047819450a9b1e315023e1d1a5,
title = "A simple proof of log-Sobolev inequalities on a path space with Gibbs measures",
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.",
keywords = "Gibbs measure, Gradient estimate, Log-Sobolev inequality, SPDE",
author = "Hiroshi Kawabi",
year = "2006",
month = "6",
day = "1",
doi = "10.1142/S021902570600238X",
language = "English",
volume = "9",
pages = "321--329",
journal = "Infinite Dimensional Analysis, Quantum Probability and Related Topics",
issn = "0219-0257",
publisher = "World Scientific Publishing Co. Pte Ltd",
number = "2",

}

TY - JOUR

T1 - A simple proof of log-Sobolev inequalities on a path space with Gibbs measures

AU - Kawabi, Hiroshi

PY - 2006/6/1

Y1 - 2006/6/1

N2 - 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.

AB - 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.

KW - Gibbs measure

KW - Gradient estimate

KW - Log-Sobolev inequality

KW - SPDE

UR - http://www.scopus.com/inward/record.url?scp=33745038536&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=33745038536&partnerID=8YFLogxK

U2 - 10.1142/S021902570600238X

DO - 10.1142/S021902570600238X

M3 - Article

VL - 9

SP - 321

EP - 329

JO - Infinite Dimensional Analysis, Quantum Probability and Related Topics

JF - Infinite Dimensional Analysis, Quantum Probability and Related Topics

SN - 0219-0257

IS - 2

ER -