Tamás Varjú (BME MI)
Horizons in multidimensional billiards.
<br><br>
Abstract: Zacherl et. al (1986) and Bleher (1992) conjectured and gave
heuristic arguments for the (weak) superdiffusivity of 2D Lorentz 
processes
with infinite horizon. In 2007, we could give a rigorous proof with D. 
Szász
and could also obtain an explicit form of the superdiffusivity coefficient
in
terms of geometric parameters of the billiard involved. In 2011, C. 
Dettmann
described heuristically the much richer horizon structure in the
multidimensional case and formulated conjectures that would lead to a
generalization of the 'simple' 2D form of the superdiffusivity 
coefficient.
Here we establish Dettmann's Conjecture 1 by simple geometric 
probabilistic
arguments. The results are joint with P. Nándori and D. Szász.