Illinois Journal of Mathematics
- Illinois J. Math.
- Volume 50, Number 1-4 (2006), 33-65.
Random walk on the incipient infinite cluster on trees
Martin T. Barlow and Takashi Kumagai
Abstract
Let $\mathcal{G}$ 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 $\mathcal{G}$; the process satisfies anomalous diffusion and has spectral dimension 4/3.
Article information
Source
Illinois J. Math., Volume 50, Number 1-4 (2006), 33-65.
Dates
First available in Project Euclid: 12 November 2009
Permanent link to this document
https://projecteuclid.org/euclid.ijm/1258059469
Digital Object Identifier
doi:10.1215/ijm/1258059469
Mathematical Reviews number (MathSciNet)
MR2247823
Zentralblatt MATH identifier
1110.60090
Subjects
Primary: 60K37: Processes in random environments
Secondary: 60J80: Branching processes (Galton-Watson, birth-and-death, etc.) 60K35: Interacting random processes; statistical mechanics type models; percolation theory [See also 82B43, 82C43]
Citation
Barlow, Martin T.; Kumagai, Takashi. Random walk on the incipient infinite cluster on trees. Illinois J. Math. 50 (2006), no. 1-4, 33--65. doi:10.1215/ijm/1258059469. https://projecteuclid.org/euclid.ijm/1258059469
