Percolation in a Hierarchical Lattice
نویسنده
چکیده
We study the percolation in the hierarchical lattice of order N where the probability of connection between two nodes separated by a distance k is of the form min{αβ−k,1}, α ≥ 0 and β > 0. We focus on the vertex degrees of the resulting percolation graph and on whether there exists an infinite component. For fixed β , we show that the critical percolation value αc(β ) is non-trivial, i.e., αc(β )∈ (0,∞), if and only if β ∈ (N,N2).
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