# Non-homogeneous persistent random walks and averaged environment for the Lévy-Lorentz gas – Giampaolo Cristadoro (Università di Milano-Bicocca)

#### Venue

Sala Riunioni (Dip. Matematica).

#### Abstract

I will first introduce a model known in the physical literature as the Lévy-Lorentz gas. The model describes the continuous-time motion of a particle on the real line in the presence of a random array of marked points, whose nearest-neighbor distances are i.i.d. and long-tailed (with finite mean but possibly infinite variance, with controlling parameter $\alpha$). I will give a brief summary of the know results about transport properties for this model. I will then present a related modelthat may be viewed as a mean-field version of the Lévy-Lorentz gas. This will naturally lead toconsider transport properties for a non-homogeneous persistent random walk.Depending on the values of $\alpha$, the model shows a transition from normal transport to superdiffusion, which is characterized by appropriate continuum limits. Joint work with Roberto Artuso, Mattia Radice and Manuele Onofri

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