Yilun Shang
The Sizes of Large Hierarchical LongRange Percolation Clusters
1434 - 1437
2011
5
8
International Journal of Mathematical and Computational Sciences
https://publications.waset.org/pdf/3332
https://publications.waset.org/vol/56
World Academy of Science, Engineering and Technology
We study a longrange percolation model in the hierarchical
lattice ΩN of order N where probability of connection between
two nodes separated by distance k is of the form minαβ−k, 1,
α ≥ 0 and β > 0. The parameter α is the percolation parameter,
while β describes the longrange nature of the model. The ΩN is
an example of so called ultrametric space, which has remarkable
qualitative difference between Euclideantype lattices. In this paper,
we characterize the sizes of large clusters for this model along the
line of some prior work. The proof involves a stationary embedding
of ΩN into Z. The phase diagram of this longrange percolation is
well understood.
Open Science Index 56, 2011