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

   
@article{ECP1612,
	author = {Yuri Mejia Miranda and Gordon Slade},
	title = {The growth constants of lattice trees and lattice animals in high dimensions},
	journal = {Electron. Commun. Probab.},
	fjournal = {Electronic Communications in Probability},
	volume = {16},
	year = {2011},
	keywords = {growth constant; lattice tree; lattice animal; mean-field model},
	abstract = {We prove that the growth constants for nearest-neighbour lattice trees and lattice (bond) animals on the integer lattice $\mathbb{Z}^d$ 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 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.},
	pages = {no. 13, 129-136},
	issn = {1083-589X},
	doi = {10.1214/ECP.v16-1612},    
        url = {http://ecp.ejpecp.org/article/view/1612}}