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2008 An extension of the inductive approach to the lace expansion
Mark Holmes, Remco van der Hofstad, Gordon Slade
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Electron. Commun. Probab. 13: 291-301 (2008). DOI: 10.1214/ECP.v13-1377


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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Mark Holmes. Remco van der Hofstad. Gordon Slade. "An extension of the inductive approach to the lace expansion." Electron. Commun. Probab. 13 291 - 301, 2008.


Accepted: 15 June 2008; Published: 2008
First available in Project Euclid: 6 June 2016

zbMATH: 1189.60177
MathSciNet: MR2415137
Digital Object Identifier: 10.1214/ECP.v13-1377

Primary: 60K35
Secondary: 82B27 , 82B41 , 82B43

Keywords: induction , Lace expansion , Lattice trees , percolation

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