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The logarithmic Sobolev inequality for the Wasserstein diffusion
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  • Published: 14 October 2008

The logarithmic Sobolev inequality for the Wasserstein diffusion

  • Maik Döring1 &
  • Wilhelm Stannat1 

Probability Theory and Related Fields volume 145, pages 189–209 (2009)Cite this article

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  • 9 Citations

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Abstract

We prove that the Dirichlet form associated with the Wasserstein diffusion on the set of all probability measures on the unit interval, introduced in von Renesse and Sturm (Entropic measure and Wasserstein diffusion. Ann Probab, 2008) satisfies a logarithmic Sobolev inequality. This implies hypercontractivity of the associated transition semigroup. We also study functional inequalities for related diffusion processes.

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References

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Authors and Affiliations

  1. Fachbereich Mathematik, Technische Universität Darmstadt, Schlossgartenstrasse 7, 64289, Darmstadt, Germany

    Maik Döring & Wilhelm Stannat

Authors
  1. Maik Döring
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  2. Wilhelm Stannat
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Correspondence to Wilhelm Stannat.

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Cite this article

Döring, M., Stannat, W. The logarithmic Sobolev inequality for the Wasserstein diffusion. Probab. Theory Relat. Fields 145, 189–209 (2009). https://doi.org/10.1007/s00440-008-0166-6

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  • Received: 29 January 2008

  • Revised: 20 June 2008

  • Published: 14 October 2008

  • Issue Date: September 2009

  • DOI: https://doi.org/10.1007/s00440-008-0166-6

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Mathematics Subject Classification (2000)

  • Primary: 58J65
  • 47D07
  • Secondary: 28A33
  • 35P15
  • 60J35
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