@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}, }