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

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

2004-01-08

arxiv.org/abs/math/0401073v1

Mathematics

Probability

26 pages, 2 figures

Scientific paper

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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