Domokos Szász
Title: On Dettmann's "horizon" conjectures

Abstract: Dettmann, in 2011, formulated three conjectures for multidimensional dispersing billiards with infinite horizon. They, in particular, support the expectation that - similarly to 2D dispersing billiards with infinite horizon - superdiffusivity matrices can be calculated simply from geometric parameters of the model. First, the conjectures, talking about the tail probabilities of the free path lengths, are generalized to semi-dispersing billiards, possibly also with corner points, and then the first two of them are settled. The results are applied to calculating the superdiffusivity covariance for the system of two hard balls on arbitrary dimensional tori and to certain cylindrical billiards. The results are joint with P. Nándori and T. Varjú.