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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.


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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
Milestones  Received 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 


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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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