The statistics of particle trajectories in the homogeneous Sinai problem for a two-dimensional lattice (Q1002816)

Consider the statistics of the free path length until the first hit of the \(h\)-neighborhood (a disk of radius \(h\)) of a nonzero integer for a particle issuing from the origin. In this paper the authors study the questions on the asymptotic behavior of the statistics while \(h \rightarrow 0\) improving and generalizing related results by F. P. Boca, R. N. Gologan, and A. Zaharescu. In particular they obtain the following: the limit distribution function for the free path length and for the sighting parameter (the distance from the trajectory to the integer point in question) does not depend on the particle escape direction (the property of isotropy).