Erwin Bolthausen, Christine Ritzmann
A Central Limit Theorem for Convolution Equations
and Weakly Self-Avoiding Walks
(117K, LATeX 2e)
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.