A local CLT for convolution equations with an application to weakly self-avoiding random walks

TL;DR

This paper establishes precise error bounds in a central limit theorem for convolution equations, with applications to high-dimensional weakly self-avoiding random walks, improving upon existing methods.

Contribution

It introduces sharper error bounds in CLT for convolution equations, specifically applied to continuous-space weakly self-avoiding random walks.

Findings

Sharper error bounds in CLT for convolution equations

Application to weakly self-avoiding random walks in high dimensions

Extension to continuous space models

Abstract

We prove error bounds in a central limit theorem for solutions of certain convolution equations. The main motivation for investigating these equations stems from applications to lace expansions, in particular to weakly self-avoiding random walks in high dimensions. As an application we treat such self-avoiding walks in continuous space. The bounds obtained are sharper than the ones obtained by other methods.