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Expansion in High Dimension for the Growth Constants of Lattice Trees and Lattice Animals
Published online by Cambridge University Press: 15 April 2013
Abstract
We compute the first three terms of the 1/d expansions for the growth constants and one-point functions of nearest-neighbour lattice trees and lattice (bond) animals on the integer lattice $\mathbb{Z}^d$, with rigorous error estimates. The proof uses the lace expansion, together with a new expansion for the one-point functions based on inclusion–exclusion.
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- Copyright © Cambridge University Press 2013
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