%0 Journal Article
	%A Yilun Shang
	%D 2011
	%J International Journal of Mathematical and Computational Sciences
	%B World Academy of Science, Engineering and Technology
	%I Open Science Index 56, 2011
	%T The Sizes of Large Hierarchical Long-Range Percolation Clusters
	%U https://publications.waset.org/pdf/3332
	%V 56
	%X We study a long-range 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 min{αβ−k, 1},
α ≥ 0 and β > 0. The parameter α is the percolation parameter,
while β describes the long-range nature of the model. The ΩN is
an example of so called ultrametric space, which has remarkable
qualitative difference between Euclidean-type 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 long-range percolation is
well understood.
	%P 1434 - 1437