Abstract:
After the first success in establishing the diffusive, Brownian limit of
planar, finite-horizon, periodic Lorentz processes, in 1981 Sinai turned
the interest toward studying models when periodicity is hurt, in
particular, to locally perturbed Lorentz processes. The 1981 solution - by
Telcs and the speaker - for a stochastic random-walk-model only led in
2009 to that for the locally perturbed, finite-horizon Lorentz process (by
Dolgopyat, Varjú and the present author). Beside reporting on these
results we also analyze the first steps in extending the super-diffusive
limit obtained for the infinite horizon periodic Lorentz process to
locally perturbed ones (results by Nándori, Paulin, Varjú and the
speaker).