Expansion in n−1 for percolation critical values on the n-cube and Z: the first three terms

Abstract

Let pc(Qn) and pc(Z) denote the critical values for nearest-neighbour bond percolation on the n-cube Qn = {0, 1}n and on Zn, respectively. Let Ω = n for G = Qn and Ω = 2n for G = Zn denote the degree of G. We use the lace expansion to prove that for both G = Qn and G = Zn, pc(G) = Ω−1 + Ω−2 + 7 2 Ω−3 + O(Ω−4). This extends by two terms the result pc(Qn… (More)

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Cite this paper

@inproceedings{Hofstad2003ExpansionIN, title={Expansion in n−1 for percolation critical values on the n-cube and Z: the first three terms}, author={Remco van der Hofstad and Gordon Slade}, year={2003} }