Extension of the generalised inductive approach to the lace expansion: Full proof

TL;DR

This paper broadens the inductive approach to the lace expansion to establish Gaussian asymptotics for models in various critical dimensions, with applications to lattice trees and potential relevance to percolation.

Contribution

It extends the inductive method for lace expansion to cover models with different critical dimensions, providing a full proof and new analytical tools.

Findings

Proves Gaussian asymptotic behaviour for models in dimensions other than 4

Applies results to lattice trees in dimensions d>8

Potential applicability to percolation in dimensions d>6

Abstract

This paper extends the inductive approach to the lace expansion of van der Hofstad and Slade in order to prove Gaussian asymptotic behaviour for models with critical dimension other than 4. The results are applied by Holmes to study sufficiently spread-out lattice trees in dimensions d>8 and may also be applicable to percolation in dimensions d>6.