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- Title
Diffusion on the Scaling Limit of the Critical Percolation Cluster in the Diamond Hierarchical Lattice.
- Authors
Hambly, B. M.; Kumagai, T.
- 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.
- Subjects
PERCOLATION; DIFFUSION; LATTICE theory; MARKOV processes; DIRICHLET forms
- Publication
Communications in Mathematical Physics, 2010, Vol 295, Issue 1, p29
- ISSN
0010-3616
- Publication type
Article
- DOI
10.1007/s00220-009-0981-3