The Scaling Limit of Lattice Trees in High Dimensions

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. Received: 27 September 1996 / Accepted: 28 July 1997