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, with rigorous error estimates. The proof uses the lace expansion, together with a new expansion for the one-point functions based on inclusion–exclusion.
(Received August 16 2012)
(Revised March 01 2013)
(Online publication April 15 2013)
2010 Mathematics subject classification:
† Supported in part by CONACYT of Mexico.
‡ Supported in part by NSERC of Canada.