Marco Lenci - Università di Bologna # Random walks in a one-dimensional Levy random environment # We consider a point process on the real line where the origin always belongs to the process and the spacings between two neighboring points are i.i.d. random variables with finite mean and infinite variance. For each realization, we study the continuous-time random walk starting at the origin and jumping between the points of the process with speed 1. This type of system is sometimes known as Levy-Lorentz gas, and we consider its quenched version. We prove a CLT and the convergence of the normally scaled moments to those of a Gaussian. As a corollary, we improve a bound of Barkai, Fleurov, Klafter (2000) on the annealed second moment (for nonequilibrium initial conditions).

Joint work with A. Bianchi, G. Cristadoro and M. Ligabò.