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On logarithmic Sobolev inequalities for continuous time random walks on graphs
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  • Published: April 2000

On logarithmic Sobolev inequalities for continuous time random walks on graphs

  • Cécile Ané1 &
  • Michel Ledoux1 

Probability Theory and Related Fields volume 116, pages 573–602 (2000)Cite this article

  • 188 Accesses

  • 28 Citations

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Abstract.

We establish modified logarithmic Sobolev inequalities for the path distributions of some continuous time random walks on graphs, including the simple examples of the discrete cube and the lattice ZZ d. Our approach is based on the Malliavin calculus on Poisson spaces developed by J. Picard and stochastic calculus. The inequalities we prove are well adapted to describe the tail behaviour of various functionals such as the graph distance in this setting.

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Authors and Affiliations

  1. Département de Mathématiques, Laboratoire de Statistique et Probabilités associé au C.N.R.S., Université Paul-Sabatier, 31062 Toulouse, France. e-mail: ane@cict.fr; ledoux@cict.fr, , , , , , FR

    Cécile Ané & Michel Ledoux

Authors
  1. Cécile Ané
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  2. Michel Ledoux
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Additional information

Received: 6 April 1998 / Revised version: 15 March 1999 / Published on line: 14 February 2000

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Ané, C., Ledoux, M. On logarithmic Sobolev inequalities for continuous time random walks on graphs. Probab Theory Relat Fields 116, 573–602 (2000). https://doi.org/10.1007/s004400050263

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  • Issue Date: April 2000

  • DOI: https://doi.org/10.1007/s004400050263

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Keywords

  • Continuous Time
  • Sobolev Inequality
  • Graph Distance
  • Stochastic Calculus
  • Tail Behaviour
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