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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classification 🧮 math.PR math.CO

keywords asymptoticcriticalcubeexpansionsmathbbpercolationvaluesbond

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

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