arXiv subjects

Christine Ritzmann

Publications and source records attributed to Christine Ritzmann.

3 recordsLinked to original sources

arXiv2014

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

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 the ones obtained by other methods.

math.PR↗

arXiv2002

Good Local Bounds for Simple Random Walks

We give a local central limit theorem for simple random walks on Z^d, including Gaussian error estimates. The detailed proof combines standard large deviation techniques with Cramer-Edgeworth expansions for lattice distributions.

math.PR↗

arXiv2002

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.

math.PR↗