A simple convergence proof for the lace expansion

2020/06/19 by Slade, Gordon
#60K35 #82B27 #82B41 #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Probability (math.PR)

paper · doi:10.48550/arxiv.2006.11241

Abstract

We use the lace expansion to give a simple proof that the critical two-point function for weakly self-avoiding walk on ℤ^d has decay |x|^-(d-2) in dimensions d>4. The proof uses elementary Fourier analysis and the Riemann--Lebesgue Lemma.

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