Diffusion on the scaling limit of the critical percolation cluster in the diamond hierarchical lattice

B. M. Hambly, T. Kumagai

Research output: Contribution to journalArticlepeer-review

19 Citations (Scopus)

Abstract

We construct critical percolation clusters on the diamond hierarchical lattice and show that the scaling limit is a graph directed random recursive fractal. A Dirichlet form can be constructed on the limit set and we consider the properties of the associated Laplace operator and diffusion process. In particular we contrast and compare the behaviour of the high frequency asymptotics of the spectrum and the short time behaviour of the on-diagonal heat kernel for the percolation clusters and for the underlying lattice. In this setting a number of features of the lattice are inherited by the critical cluster.

Original languageEnglish
Pages (from-to)29-69
Number of pages41
JournalCommunications in Mathematical Physics
Volume295
Issue number1
DOIs
Publication statusPublished - 2010 Feb
Externally publishedYes

ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Mathematical Physics

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