Random Walk on The Incipient Infinite Cluster on Trees

Martin T. Barlow*, Takashi Kumagai

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

56 Citations (Scopus)


Let script G sign be the incipient infinite cluster (IIC) for percolation on a homogeneous tree of degree n0 + 1. We obtain estimates for the transition density of the continuous time simple random walk Y on script G sign; the process satisfies anomalous diffusion and has spectral dimension 4/3.

Original languageEnglish
Pages (from-to)33-65
Number of pages33
JournalIllinois Journal of Mathematics
Issue number1
Publication statusPublished - 2006
Externally publishedYes

ASJC Scopus subject areas

  • General Mathematics


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