Random Walk on The Incipient Infinite Cluster on Trees

Martin T. Barlow; Takashi Kumagai

doi:10.1215/ijm/1258059469

Random Walk on The Incipient Infinite Cluster on Trees

Martin T. Barlow^*, Takashi Kumagai

^*Corresponding author for this work

Research output: Contribution to journal › Article › peer-review

52 Citations (Scopus)

Abstract

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 language	English
Pages (from-to)	33-65
Number of pages	33
Journal	Illinois Journal of Mathematics
Volume	50
Issue number	1
DOIs	https://doi.org/10.1215/ijm/1258059469
Publication status	Published - 2006
Externally published	Yes

ASJC Scopus subject areas

Mathematics(all)

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title = "Random Walk on The Incipient Infinite Cluster on Trees",

abstract = "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.",

author = "Barlow, {Martin T.} and Takashi Kumagai",

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journal = "Illinois Journal of Mathematics",

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AU - Barlow, Martin T.

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AB - 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.

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JO - Illinois Journal of Mathematics

JF - Illinois Journal of Mathematics

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Random Walk on The Incipient Infinite Cluster on Trees

Abstract

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