Lace expansion for dummies

2015/12/04 by Erwin Bolthausen, Remco van der Hofstad, Bolthausen, Erwin +3 · 1 citation
Mathematics · Computer Science · #Advanced Harmonic Analysis Research #Advanced Mathematical Modeling in Engineering #Nonlinear Partial Differential Equations

paper · pdf · doi:10.48550/arxiv.1512.01481

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.

Citations

• Green's Functions for Random Walks on ZN

Cited by

• Capacity of the range of random walk: Moderate deviations in dimensions 4 and 5

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