Tail asymptotics of free path lengths for the periodic Lorentz process. On Dettmann's geometric conjectures

Peter Nandori, Domokos Szasz, Tamas Varju

In the simplest case, consider a ${\mathbb{Z}}^d$-periodic ($d\ge 3$) arrangement of balls of radii < 1/2, and select a random direction and point (outside the balls). According to…