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

• Avena, Luca ^[1] ; Bolthausen, Erwin ^[2] ; Ritzmann, Christine ^[3]
  1. [1] Leiden University

     Leiden University

     Países Bajos

     
  2. [2] University Zürich
  3. [3] Zürich Versicherungen

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• Localización: Annals of probability: An official journal of the Institute of Mathematical Statistics, ISSN 0091-1798, Vol. 44, Nº. 1, 2016, págs. 206-234
• Idioma: inglés
• DOI: 10.1214/14-AOP971
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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.