%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