Non-homogeneous persistent random walks and Lévy-Lorentz gas

We consider transport properties for a non-homogeneous persistent random walk, that may be viewed as a mean-field version of the Lévy-Lorentz gas, namely a 1D model characterized by a fat polynomial tail of the distribution of scatterers' distance, with parameter μ. By varying the value of μ we have a transition from normal transport to superdiffusion, which we characterize by appropriate continuum limits.