In a flat 2-torus with a disk of diameter r removed, let Φr​(t) be the
distribution of free-path lengths (the probability that a segment of length
larger than t with uniformly distributed origin and direction does not meet
the disk).
We prove that Φr​(t/r) behaves like π2t2​ for each t>2
and in the limit as r→0+, in some appropriate sense.
We then discuss the implications of this result in the context of kinetic
theory.Comment: 26 pages, 5 figures, to be published in Commun. Math. Phy