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Random Walks on Percolation Clusters

  • Markus HeydenreichEmail author
  • Remco van der Hofstad
Chapter
Part of the CRM Short Courses book series (CRMSC)

Abstract

Random structures have an intricate relationship with the random walks defined on them. Here we focus on random walks on percolation clusters as a prime example of the random conductance model with the additional charm of not being elliptic. We discuss random walks on supercritical percolation clusters, on finite critical clusters, and on the incipient infinite cluster. The results show that random walks on supercritical and critical percolation structures behave completely differently, underlining the remarkable features of critical structures.

Copyright information

© Springer International Publishing Switzerland 2017

Authors and Affiliations

  1. 1.Mathematisches InstitutLudwig-Maximilians-Universität MünchenMünchenGermany
  2. 2.Department of Mathematics and Computer ScienceEindhoven University of TechnologyEindhovenThe Netherlands

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