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arXiv · 1303.3034

An asymptotic estimate of the variance of the self-intersections of a planar periodic Lorentz process

Francoise Pene
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Abstract

We consider a periodic planar Lorentz process with strictly convex obstacles and finite horizon. This process describes the displacement of a particle moving in the plane with unit speed and with elastic reflection on the obstacles. We call number of self-intersections of this Lorentz process the number V(n) of couples of integers (k,m) smaller than n such that the particle hits a same obstacle both at the k-th and at the m-th collision times. The aim of this paper is to prove that the variance of V(n) is equivalent to cn^2 (such a result has recently been proved for simple planar random walks by Deligiannidis and Utev).

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Francoise Pene. 2013-03-12. An asymptotic estimate of the variance of the self-intersections of a planar periodic Lorentz process. https://arxiv.org/abs/1303.3034

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