The Einstein Relation for the Variable-Range Hopping model

SALVI Michele
Localisation: Université Paris Dauphine, France
Type: Groupe de travail probabilités
Site: UPEC
P2 131
Date de début:
05/12/2017 - 13:45
Date de fin:
05/12/2017 - 13:45

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 long-range 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 model.