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

Remco van der Hofstad·Gordon Slade
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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 $n^{-1}$.

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Remco van der Hofstad, Gordon Slade. 2004-01-08. Asymptotic expansions in $n^{-1}$ for percolation critical values on the $n$-cube and $\mathbb{Z}^n$. https://arxiv.org/abs/math/0401073

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