An asymptotic variance of the self-intersections of random walks
Probability
2015-03-17 v1
Abstract
We present a Darboux-Wiener type lemma and apply it to obtain an exact asymptotic for the variance of the self-intersection of one and two-dimensional random walks. As a corollary, we obtain a central limit theorem for random walk in random scenery conjectured by Kesten and Spitzer in 1979.
Keywords
Cite
@article{arxiv.1004.4845,
title = {An asymptotic variance of the self-intersections of random walks},
author = {George Deligiannidis and Sergey Utev},
journal= {arXiv preprint arXiv:1004.4845},
year = {2015}
}