The periodic Lorentz gas in the Boltzmann-Grad limit: the free path length and the K-S entropy

Abstract

We study the periodic Lorentz gas in the Boltzmann-Grad limit, whose convergence was rigorously established in the seminal work of Marklof-Str\"ombergsson. Extending the two dimensional results of Boca-Zaharescu to higher dimensions, we present a more detailed description of this convergence. More precisely, we derive the asymptotic formula of the distribution function of the free path length; and we explicitly compute the constant in the asymptotic formula for the Kolmogorov-Sinai (K-S) entropy of the billiard map.