The growth constants of lattice trees and lattice animals in high dimensions

Yuri Mejia Miranda; Gordon Slade

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arXiv · 1102.3682

The growth constants of lattice trees and lattice animals in high dimensions

Yuri Mejia Miranda·Gordon Slade

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Abstract

We prove that the growth constants for nearest-neighbour lattice trees and lattice (bond) animals on the integer lattice Zd are asymptotic to 2de as the dimension goes to infinity, and that their critical one-point functions converge to e. Similar results are obtained in dimensions d>8 in the limit of increasingly spread-out models; in this case the result for the growth constant is a special case of previous results of M. Penrose. The proof is elementary, once we apply previous results of T. Hara and G. Slade obtained using the lace expansion.

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Yuri Mejia Miranda, Gordon Slade. 2011-02-17. The growth constants of lattice trees and lattice animals in high dimensions. https://arxiv.org/abs/1102.3682

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