An asymptotic variance of the self-intersections of random walks

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.

Cited by in corpus (4)

• An asymptotic estimate of the variance of the self-intersections of a planar periodic Lorentz process
• Optimal bounds for self-intersection local times
• Self-intersections of trajectories of Lorentz process
• Renewal theorems for random walks in random scenery