Lace expansion for dummies

Abstract

We show Green's function asymptotic upper bound for the two-point function of weakly self-avoiding walk in dimension bigger than 4, revisiting a classic problem. Our proof relies on Banach algebras to analyse the lace-expansion fixed point equation and is simpler than previous approaches in that it avoids Fourier transforms.

Full proof in just 14 pages. New version corrects a few glitches

References in corpus (1)

• Application of the lace expansion to the ${\phi }^4$ model