The Annals of Probability

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

Luca Avena, Erwin Bolthausen, and Christine Ritzmann

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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 those obtained by other methods.

Article information

Ann. Probab., Volume 44, Number 1 (2016), 206-234.

Received: February 2014
First available in Project Euclid: 2 February 2016

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Zentralblatt MATH identifier

Primary: 60K35: Interacting random processes; statistical mechanics type models; percolation theory [See also 82B43, 82C43]
Secondary: 60F05: Central limit and other weak theorems

Central limit theorem convolution equations self-avoiding random walks


Avena, Luca; Bolthausen, Erwin; Ritzmann, Christine. A local CLT for convolution equations with an application to weakly self-avoiding random walks. Ann. Probab. 44 (2016), no. 1, 206--234. doi:10.1214/14-AOP971.

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