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An asymptotic variance of the self-intersections of random walks

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.

preprint2010arXivOpen access
George DeligiannidisSergey Utev
math.PR
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Open access2 authors1 topic
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George DeligiannidisSergey Utev

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