Expansion for the critical point of site percolation: the first three terms

Abstract

We expand the critical point for site percolation on the d-dimensional hypercubic lattice in terms of inverse powers of 2d, and we obtain the first three terms rigorously. This is achieved using the lace expansion.

Critical site percolation in high dimension

“…This is the content of a forthcoming paper [15]. The idea to derive p c expansions from lace expansion coefficients has been earlier achieved for bond percolation by Hara and Slade [14] and van der Hofstad and Slade [23].…”