Limit theorems for self-intersecting trajectories in Z-extensions

Abstract

This paper studies for a class of Z-extensions of dynamical systems including Z-periodic Lorentz gas the asymptotic behavior of the number of self-intersections of the trajectory of the flow. It concludes on a functional limit theorem for the auto-intersection process by studying Skorohod convergence of discrete local time of a dynamical random walk toward the local time of a Brownian motion.