# American Institute of Mathematical Sciences

November  2014, 34(11): 4781-4806. doi: 10.3934/dcds.2014.34.4781

## Self-intersections of trajectories of the Lorentz process

 1 Université de Brest, UMR CNRS 6205, Laboratoire de Mathématique de Bretagne Atlantique, 6 avenue Le Gorgeu, 29238 Brest cedex, France

Received  April 2013 Revised  February 2014 Published  May 2014

We are interested in the asymptotic behaviour of the number of self-intersections of a trajectory of a Lorentz process in a $\mathbb Z^2$-periodic planar domain with strictly convex obstacles and with finite horizon. We give precise estimates for its expectation and its variance. As a consequence, we establish the almost sure convergence of the self-intersections with a suitable normalization.
Citation: Françoise Pène. Self-intersections of trajectories of the Lorentz process. Discrete & Continuous Dynamical Systems, 2014, 34 (11) : 4781-4806. doi: 10.3934/dcds.2014.34.4781
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