Isoperimetry and heat kernel decay on percolation clusters

• Pierre Mathieu ^[2] ; Elisabeth Remy ^[1]
  1. [1] Fraunhofer Institute for Material Flow and Logistics

     Fraunhofer Institute for Material Flow and Logistics

     Kreisfreie Stadt Dortmund, Alemania

     
  2. [2] CMI
• Localización: Annals of probability: An official journal of the Institute of Mathematical Statistics, ISSN 0091-1798, Vol. 32, Nº. 1, 1, 2004, págs. 100-128
• Idioma: inglés
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• Resumen

  • We prove that the heat kernel on the infinite Bernoulli percolation cluster in \Zd almost surely decays faster than t−d/2. We also derive estimates on the mixing time for the random walk confined to a finite box. Our approach is based on local isoperimetric inequalities. Some of the results of this paper were previously announced in the note of Mathieu and Remy [C. R. Acad. Sci. Paris Sér. I Math. 332 (2001) 927--931].