@article{EJP499,
author = {Mark Holmes},
title = {Convergence of Lattice Trees to Super-Brownian Motion above the Critical Dimension},
journal = {Electron. J. Probab.},
fjournal = {Electronic Journal of Probability},
volume = {13},
year = {2008},
keywords = {Lattice trees; super-Brownian motion; lace expansion.},
abstract = {We use the lace expansion to prove asymptotic formulae for the Fourier transforms of the $r$-point functions for a spread-out model of critically weighted lattice trees on the $d$-dimensional integer lattice for $d > 8$. A lattice tree containing the origin defines a sequence of measures on the lattice, and the statistical mechanics literature gives rise to a natural probability measure on the collection of such lattice trees. Under this probability measure, our results, together with the appropriate limiting behaviour for the survival probability, imply convergence to super-Brownian excursion in the sense of finite-dimensional distributions.},
pages = {no. 23, 671-755},
issn = {1083-6489},
doi = {10.1214/EJP.v13-499},
url = {http://ejp.ejpecp.org/article/view/499}}