**Abstract:**

The Mott Variable-Range Hopping model is considered in Physics as an accurate representation of electrical conduction in semiconductors. From the mathematical point of view, it represents a prominent example of reversible longrange random walks on random point processes, which generalize in several ways the classical random conductance model on the lattice. We ask ourselves how an external field influences the limiting velocity of the walk: So far, only very few models of biased random walks with trapping mechanisms have been rigorously studied. An accurate control of the invariant measure for the process from the point of view of the particle will remarkably allow us to go a step further and prove the Einstein Relation – the equivalence of mobility and diffusivity of the walk. This is a joint work with Alessandra Faggionato (La Sapienza) and Nina Gantert (TU Munich).

**Biography:**

Michele Salvi is a Postdoc in Mathematics at École Polytechnique and INRA with the ANR CADENCE. From 2016 to 2018 he had a Marie Skłodowska-Curie fellowship at Paris-Dauphine University. His main interest is probability theory. In particular, he is working at the moment on different models of random processes, often evolving in a random medium, and of random graphs with applications in physics, computer science and biology.

*Seminar by the NYU-ECNU Institute of Mathematical Sciences at NYU Shanghai*