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Push-Forward Measures on Configuration Spaces: Integration by Parts and Log-Sobolev Inequality

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Abstract

We study a class of measures on the space \(\Gamma _{X}\) of locally finite configurations 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 and log-Sobolev inequality.

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Acknowledgments

We would like thank Z. Brzezniak, Yu. Kondratiev and E. Lytvynov for their interest to this work and stimulating discussions.

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Authors and Affiliations

  1. Department of Mathematics, The University of York, York, YO1 5DD, UK

    Alexei Daletskii

  2. Department of Mathematics, Quaid i Azam University, Islamabad, Pakistan

    Ahsan Ul Haq

Authors
  1. Alexei Daletskii
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  2. Ahsan Ul Haq
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Correspondence to Alexei Daletskii.

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Communicated by Yuri Kondratiev.

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Daletskii, A., Ul Haq, A. Push-Forward Measures on Configuration Spaces: Integration by Parts and Log-Sobolev Inequality. Complex Anal. Oper. Theory 9, 1533–1555 (2015). https://doi.org/10.1007/s11785-014-0406-y

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  • DOI: https://doi.org/10.1007/s11785-014-0406-y

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