Journal article

An extension of the inductive approach to the lace expansion

Remco Van Der Hofstad, Mark Holmes, Gordon Slade

ELECTRONIC COMMUNICATIONS IN PROBABILITY | UNIV WASHINGTON, DEPT MATHEMATICS | Published : 2008

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. © 2008 Applied Probability Trust.

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