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.
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Received: 27 September 1996 / Accepted: 28 July 1997
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Derbez, E., Slade, G. The Scaling Limit of Lattice Trees in High Dimensions . Comm Math Phys 193, 69–104 (1998). https://doi.org/10.1007/s002200050319
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DOI: https://doi.org/10.1007/s002200050319