Marco Lenci (Università di Bologna)

Dynamics, Geometry and Groups Seminar

Thursday, August 11th, 2022

Time: 2:30 p.m.  Place: Jeffery Hall 422

Speaker: Marco Lenci (Università di Bologna)

Title: Random walks in one-dimensional Lévy random media

Abstract: One speaks of anomalous diffusion when a process (e.g., a mechanical system of particles or a stochastic process) diffuses through space with a different law than that of the Brownian motion. These types of systems are observed both in physics (rarefied gases, certain glassy materials, etc.) and in other sciences (e.g., ethology, social sciences, financial mathematics, etc.). The most realistic models of anomalous diffusion are those where the anomalous behavior is caused by particular properties of the media the process lives in. The mathematical literature on such systems is rather scant. We present a continuous-time random walk in random medium which generalizes a system known in the physical literature as Lévy-Lorentz Gas: a particle travels at constant speed between “target points” that are randomly placed on the real line with fat-tailed interdistances. Depending on the decay of the tail of the distribution, this process may exhibit different types of anomalous diffusion.