Limit theorems for self-intersecting trajectories in Z-extensions
Dynamical Systems
2023-12-29 v3
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.
Keywords
Cite
@article{arxiv.2201.01980,
title = {Limit theorems for self-intersecting trajectories in Z-extensions},
author = {Phalempin Maxence},
journal= {arXiv preprint arXiv:2201.01980},
year = {2023}
}