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

Hiroshi Kawabi

doi:10.1142/S021902570600238X

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

Hiroshi Kawabi

Research output: Contribution to journal › Article › peer-review

2 Citations (Scopus)

Abstract

In this paper, we give a simple proof of log-Sobolev inequalities on an infinite volume path space C(ℝ, ℝ^d) 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 language	English
Pages (from-to)	321-329
Number of pages	9
Journal	Infinite Dimensional Analysis, Quantum Probability and Related Topics
Volume	9
Issue number	2
DOIs	https://doi.org/10.1142/S021902570600238X
Publication status	Published - 2006 Jun
Externally published	Yes

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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10.1142/S021902570600238X

Cite this

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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",

note = "Funding Information: I am grateful to Professor Tadahisa Funaki for sending me his manuscript Ref. 5 before publication. I also thank Professor Michael R{\"o}ckner for his interest and invitation to University of Bielefeld. The results of this paper were reported at Bielefeld and Bonn in Fall 2004. I was supported by Research Fellowships of the Japan Society for the Promotion of Science for Young Scientists and by Grant-in-Aid for Scientific research 15-3706, Japan Society for the Promotion of Science, Japan. Copyright: Copyright 2008 Elsevier B.V., All rights reserved.",

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doi = "10.1142/S021902570600238X",

language = "English",

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PY - 2006/6

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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.

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KW - Gradient estimate

KW - Log-Sobolev inequality

KW - SPDE

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JF - Infinite Dimensional Analysis, Quantum Probability and Related Topics

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

Abstract

Keywords

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