@article{(Open Science Index):https://publications.waset.org/pdf/3332,
	  title     = {The Sizes of Large Hierarchical Long-Range Percolation Clusters},
	  author    = {Yilun Shang},
	  country	= {},
	  institution	= {},
	  abstract     = {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 minαβ−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.},
	    journal   = {International Journal of Mathematical and Computational Sciences},
	  volume    = {5},
	  number    = {8},
	  year      = {2011},
	  pages     = {1434 - 1437},
	  ee        = {https://publications.waset.org/pdf/3332},
	  url   	= {https://publications.waset.org/vol/56},
	  bibsource = {https://publications.waset.org/},
	  issn  	= {eISSN: 1307-6892},
	  publisher = {World Academy of Science, Engineering and Technology},
	  index 	= {Open Science Index 56, 2011},
	}