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We prove that the growth constants for nearest-neighbour lattice trees and lattice (bond) animals on the integer lattice d 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… (More)

- Yuri Mejía Miranda, Gordon Slade
- Combinatorics, Probability & Computing
- 2013

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 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. 1 Main… (More)

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