A Central Limit Theorem for Convolution Equations and Weakly Self-Avoiding Walks

2001/03/30 by Erwin Bolthausen, Bolthausen, Erwin, Christine Ritzmann +1
Mathematics · Physics and Astronomy · #60K35 #82B41 #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Probability (math.PR) #math-ph #math.MP #math.PR #msc:60K35 #msc:82B41

paper · pdf · doi:10.48550/arxiv.math/0103218

35 pages, LaTeX2e

arxiv created 2002/01/11 · arxiv updated 2009/11/30

Abstract

The main result of this paper is a general central limit theorem for distributions defined by certain renewal type equations. We apply this to weakly self-avoiding random walks. We give good error estimates and Gaussian tail estimates which have not been obtained by other methods. We use the lace expansion and at the same time develop a new perspective on this method: We work with a fixed point argument directly in the x-space without using Laplace or Fourier transformation.

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