A Note on the Perturbation of Mixed Percolation on the Hierarchical Group

作者：Shang Yilun^*

来源：Zeitschrift fur Naturforschung Section A-A Journal of Physical Sciences, 2013, 68(6-7): 475-478.

DOI：10.5560/ZNA.2013-0015

• Mixed Percolation
• Hierarchical Group
• Percolation Function

We study mixed percolation on the hierarchical group of order N where each node is open with probability 1 - gamma, 0 %26lt;= gamma %26lt;= 1, and the probability of connection between two open nodes separated by a distance k is of the form 1 - exp(-alpha beta(-k)), alpha %26gt;= 0, and beta %26gt; 0. The parameters alpha and gamma are the percolation parameters, while beta describes the long-range nature of the model. In terms of parameters alpha, beta, and gamma, we show some perturbation results for the percolation function theta(alpha, beta, gamma), which is the probability of existing an infinite component containing a prescribed node.

• 出版日期2013-7