An extension of the inductive approach to the lace expansion

Mark P Holmes (University of Auckland)
Remco van der Hofstad (Eindhoven University of Technology)
Gordon Slade (University of British Columbia)

Abstract


We extend the inductive approach to the lace expansion, previously developed to study models with critical dimension 4, to be applicable more generally. In particular, the result of this note has recently been used to prove Gaussian asymptotic behaviour for the Fourier transform of the two-point function for sufficiently spread-out lattice trees in dimensions $d > 8$, and it is potentially also applicable to percolation in dimensions $d > 6$.

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Pages: 291-301

Publication Date: June 15, 2008

DOI: 10.1214/ECP.v13-1377

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