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arXiv · 1208.3513

Expansion in high dimension for the growth constants of lattice trees and lattice animals

Yuri Mejia Miranda·Gordon Slade
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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 Zd, 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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Yuri Mejia Miranda, Gordon Slade. 2012-08-16. Expansion in high dimension for the growth constants of lattice trees and lattice animals. https://arxiv.org/abs/1208.3513

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