Eric Derbez, Gordon Slade.
Lattice trees and super-Brownian motion.
(63K, tex)

ABSTRACT.  This article discusses our recent proof that above eight dimensions 
the scaling limit of sufficiently spread-out
lattice trees is the variant of super-Brownian motion called
integrated super-Brownian excursion (ISE), 
as conjectured by Aldous.  
The same is true for nearest-neighbour lattice trees in sufficiently
high dimensions.
The proof, whose details will appear elsewhere, 
uses the lace expansion.  Here, a related but simpler analysis is applied to
show that the scaling limit of a mean-field theory is ISE, in all dimensions.  
A connection is drawn between ISE and 
certain generating functions and 
critical exponents, which may be useful for the
study of high-dimensional percolation models at the critical point.