Asymptotic expansions in $n^{-1}$ for percolation critical values on the $n$-cube and $\mathbb{Z}^n$

Abstract

We use the lace expansion to prove that the critical values for nearest-neighbour bond percolation on the $n$-cube $\{0,1\}^n$ and on $\mathbb{Z}^n$ have asymptotic expansions, with rational coefficients, to all orders in powers of $n^{-1}$.