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

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

2001-03-30

arxiv.org/abs/math/0103218v2

Mathematics

Probability

35 pages, LaTeX2e

Scientific paper

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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