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Poincaré and logarithmic Sobolev inequality for Ginzburg-landau processes in random environment
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  • Published: 05 July 2004

Poincaré and logarithmic Sobolev inequality for Ginzburg-landau processes in random environment

  • C. Landim1 &
  • J. Noronha Neto2 

Probability Theory and Related Fields volume 131, pages 229–260 (2005)Cite this article

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Abstract.

We consider reversible, conservative Ginzburg–Landau processes in a random environment, whose potential are bounded perturbations of the Gaussian potential, evolving on a d-dimensional cube of length L. We prove in all dimensions that the spectral gap of the generator and the logarithmic Sobolev constant are of order L−2 almost surely with respect to the environment.

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Author information

Authors and Affiliations

  1. IMPA, Estrada Dona Castorina 110, CEP 22460 Rio de Janeiro, Brasil and CNRS UMR 6085, Université de Rouen, 76128, Mont Saint Aignan, France

    C. Landim

  2. IMPA, Estrada Dona Castorina 110, CEP, 22460, Rio de Janeiro, Brasil

    J. Noronha Neto

Authors
  1. C. Landim
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  2. J. Noronha Neto
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Corresponding author

Correspondence to C. Landim.

Additional information

Acknowledgement The authors wish to thank J. Quastel and H. T. Yau for the private communication of the unpublished manuscript [21]

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Landim, C., Noronha Neto, J. Poincaré and logarithmic Sobolev inequality for Ginzburg-landau processes in random environment. Probab. Theory Relat. Fields 131, 229–260 (2005). https://doi.org/10.1007/s00440-004-0370-y

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  • Received: 30 March 2003

  • Revised: 17 March 2004

  • Published: 05 July 2004

  • Issue Date: February 2005

  • DOI: https://doi.org/10.1007/s00440-004-0370-y

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Key words or phrases:

  • Spectral Gap
  • Logarithmic Sobolev Inequality
  • Random Environment
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