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

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.