## The Annals of Probability

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

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

Luca Avena, Erwin Bolthausen, and Christine Ritzmann

#### 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 those obtained by other methods.

#### Article information

**Source**

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

**Dates**

Received: February 2014

First available in Project Euclid: 2 February 2016

**Permanent link to this document**

https://projecteuclid.org/euclid.aop/1454423039

**Digital Object Identifier**

doi:10.1214/14-AOP971

**Mathematical Reviews number (MathSciNet)**

MR3456336

**Zentralblatt MATH identifier**

1343.60009

**Subjects**

Primary: 60K35: Interacting random processes; statistical mechanics type models; percolation theory [See also 82B43, 82C43]

Secondary: 60F05: Central limit and other weak theorems

**Keywords**

Central limit theorem convolution equations self-avoiding random walks

#### Citation

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. https://projecteuclid.org/euclid.aop/1454423039