Open Access

# Logarithmic Sobolev inequality for a class of measures on configuration spaces

### Abstract

We study a class of measures on the space $\Gamma _{X}$ of locally finiteconfi\-gurations in $X=\mathbb{R}^{d}$, obtained as images of ''lattice'' Gibbs measures on $X^{\mathbb{Z}^{d}}$ with respect to an embedding $\mathbb{Z}^{d}\subset \mathbb{R}^{d}$. For these measures, we prove the integration by parts formula andlog-Sobolev inequality.

Key words: Configuration space, log-Sobolev inequality, integration by parts formula, Gibbs measure.

### Article Information

 Title Logarithmic Sobolev inequality for a class of measures on configuration spaces Source Methods Funct. Anal. Topology, Vol. 19 (2013), no. 4, 293-300 MathSciNet MR3156295 zbMATH 1313.46050 Milestones Received 16/09/2013 Copyright The Author(s) 2013 (CC BY-SA)

### Authors Information

Alexei Daletskii
Department of Mathematics, University of York, Heslington, York, YO10 5DD, UK

Ahsan Ul Haq
Department of Mathematics, University of York, Heslington, York, YO10 5DD, UK

### Citation Example

Alexei Daletskii and Ahsan Ul Haq, Logarithmic Sobolev inequality for a class of measures on configuration spaces, Methods Funct. Anal. Topology 19 (2013), no. 4, 293-300.

### BibTex

@article {MFAT708,
AUTHOR = {Daletskii, Alexei and Ul Haq, Ahsan},
TITLE = {Logarithmic Sobolev inequality for a class of measures on configuration spaces},
JOURNAL = {Methods Funct. Anal. Topology},
FJOURNAL = {Methods of Functional Analysis and Topology},
VOLUME = {19},
YEAR = {2013},
NUMBER = {4},
PAGES = {293-300},
ISSN = {1029-3531},
MRNUMBER = {MR3156295},
ZBLNUMBER = {1313.46050},
URL = {http://mfat.imath.kiev.ua/article/?id=708},
}