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Random walk on the incipient infinite cluster on trees

Martin T. Barlow·Takashi Kumagai
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Abstract

Let ${\cal G}$ be the incipient infinite cluster (IIC) for percolation on a homogeneous tree of degree $n_0+1$. We obtain estimates for the transition density of the continuous time simple random walk $Y$ on ${\cal G}$; the process satisfies anomalous diffusion and has spectral dimension 4/3.

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Martin T. Barlow, Takashi Kumagai. 2005-03-07. Random walk on the incipient infinite cluster on trees. https://arxiv.org/abs/math/0503118

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