Eric Derbez, Gordon Slade.
The scaling limit of lattice trees in high dimensions.
(122K, Latex)
ABSTRACT. We prove that above eight dimensions the scaling limit
of sufficiently spread-out
lattice trees is the variant of super-Brownian motion known as
integrated super-Brownian excursion (ISE),
as conjectured by Aldous.
The same is true for nearest-neighbour lattice trees in sufficiently
high dimensions.
The proof uses the lace expansion.