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

2013/01/25 by Luca Avena, Erwin Bolthausen, Avena, Luca +3
Economics, Econometrics and Finance · Mathematics · #FOS: Mathematics #Mathematical Dynamics and Fractals #Probability (math.PR) #Stochastic processes and financial applications #Stochastic processes and statistical mechanics #math.PR

paper · pdf · doi:10.48550/arxiv.1301.6071

28 pages, 2 figures

openalex publication_date 2013/01/25 · arxiv created 2014/04/10 · arxiv updated 2014/04/11 · openalex created_date 2022/10/03 · openalex updated_date 2026/07/28

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.

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