Journal of Theoretical Probability

, Volume 21, Issue 4, pp 910–935 | Cite as

Heat Kernel Estimates for Strongly Recurrent Random Walk on Random Media

  • Takashi Kumagai
  • Jun Misumi


We establish general estimates for simple random walk on an arbitrary infinite random graph, assuming suitable bounds on volume and effective resistance for the graph. These are generalizations of the results in Barlow et al. (Commun. Math. Phys. 278:385–431, 2008, Sects. 1, 2) and in particular imply the spectral dimension of the random graph. We will also give an application of the results to random walk on a long-range percolation cluster.


Random walk Random media Heat kernel estimates Spectral dimension Long-range percolation 

Mathematics Subject Classification (2000)

60J45 05C80 35K05 82B43 


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Copyright information

© Springer Science+Business Media, LLC 2008

Authors and Affiliations

  1. 1.Department of MathematicsKyoto UniversityKyotoJapan
  2. 2.Graduate School of Mathematical SciencesThe University of TokyoTokyoJapan

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