We prove a sufficient set of conditions for a sequence of finite measures on the space of cadlag measure-valued paths to converge to the canonical measure of super-Brownian motion in the sense of convergence of finite-dimensional distributions. The conditions are convergence of the Fourier transform of the r-point functions and perhaps convergence of the “survival probabilities.” These conditions have recently been shown to hold for a variety of statistical mechanical models, including critical oriented percolation, the critical contact process and lattice trees at criticality, all above their respective critical dimensions.
@article{1189000927,
author = {Holmes, Mark and Perkins, Edwin},
title = {Weak convergence of measure-valued processes and r-point functions},
journal = {Ann. Probab.},
volume = {35},
number = {1},
year = {2007},
pages = { 1769-1782},
language = {en},
url = {http://dml.mathdoc.fr/item/1189000927}
}
Holmes, Mark; Perkins, Edwin. Weak convergence of measure-valued processes and r-point functions. Ann. Probab., Tome 35 (2007) no. 1, pp. 1769-1782. http://gdmltest.u-ga.fr/item/1189000927/