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

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

2011-02-17

arxiv.org/abs/1102.3682v1

Mathematics

Probability

8 pages, 1 figure

Scientific paper

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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