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Logarithmic Sobolev inequality for a class of measures on configuration spaces

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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.


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Article Information

TitleLogarithmic Sobolev inequality for a class of measures on configuration spaces
SourceMethods Funct. Anal. Topology, Vol. 19 (2013), no. 4, 293-300
MathSciNet MR3156295
zbMATH 1313.46050
MilestonesReceived 16/09/2013
CopyrightThe 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},
}


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