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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

YURI MEJÍA MIRANDA  and
GORDON SLADE
YURI MEJÍA MIRANDA
Affiliation:
Department of Mathematics, University of British Columbia, Vancouver, BC, CanadaV6T 1Z2 (e-mail: amie.yuri@gmail.com, slade@math.ubc.ca)
GORDON SLADE
Affiliation:
Department of Mathematics, University of British Columbia, Vancouver, BC, CanadaV6T 1Z2 (e-mail: amie.yuri@gmail.com, slade@math.ubc.ca)
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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 $\mathbb{Z}^d$, with rigorous error estimates. The proof uses the lace expansion, together with a new expansion for the one-point functions based on inclusion–exclusion.

Keywords

Primary 60K35Secondary 82B41

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Type
Paper
Information
Combinatorics, Probability and Computing , Volume 22 , Issue 4 , July 2013 , pp. 527 - 565
Copyright
Copyright © Cambridge University Press 2013 

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