An asymptotic variance of the self-intersections of random walks

Details An asymptotic variance of the self-intersections of random walks An asymptotic variance of the self-intersections of random walks

2010-04-27

arxiv.org/abs/1004.4845v1

Mathematics

Probability

Scientific paper

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.

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