Asymptotic expansions in n-1 for percolation critical values on the n-cube and Zn

Authors:
Remco van der Hofstad;Gordon Slade
Affiliations:
Department of Mathematics and Computer Science, Eindhoven University of Technology, MB Eindhoven, The Netherlands;Department of Mathematics, University of British Columbia, Vancouver, British Columbia, Canada
Venue:
Random Structures & Algorithms
Year:
2005

Citing 4
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Abstract

We use the lace expansion to prove that the critical values for nearest-neighbor bond percolation on the n-cube {0, 1}n and on the integer lattice Zn have asymptotic expansions, with rational coefficients, to all orders in powers of n-1.