Asymptotic expansions in \(n^{-1}\) for percolation critical values on the \(n\)-cube and \(\mathbb Z^n\). (English) Zbl 1077.60077
Summary: We use the lace expansion to prove that the critical values for nearest-neighbor bond percolation on the \(n\)-cube \(\{0, 1\}^{n}\) and on the integer lattice \(\mathbb Z^{n}\) have asymptotic expansions, with rational coefficients, to all orders in powers of \(n^{-1}\).
MSC:
| 60K35 | Interacting random processes; statistical mechanics type models; percolation theory |
| 82B43 | Percolation |
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