Geodesic
Lattice trees and super-Brownian motion
Canadian mathematical bulletin, Tome 40 (1997) no. 1, pp. 19-38

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DOI

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.
DOI : 10.4153/CMB-1997-003-8
Mots-clés : Primary: 82B41, 60K35, 60J65 
Derbez, Eric; Slade, Gordon. Lattice trees and super-Brownian motion. Canadian mathematical bulletin, Tome 40 (1997) no. 1, pp. 19-38. doi: 10.4153/CMB-1997-003-8
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     doi = {10.4153/CMB-1997-003-8},
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