TY - JFULL
AU - Yilun Shang
PY - 2011/9/
TI - The Sizes of Large Hierarchical Long-Range Percolation Clusters
T2 - International Journal of Mathematical and Computational Sciences
SP - 1433
EP - 1437
VL - 5
SN - 1307-6892
UR - https://publications.waset.org/pdf/3332
PU - World Academy of Science, Engineering and Technology
NX - Open Science Index 56, 2011
N2 - 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.
ER -