Mott variable range hopping is a basic mechanism of electron transport in strongly
disordered solids. In a mean field approximation, the mathematical model is given by a
random walk on a simple point process of R^d with points marked by energy random variables. Jumps can be arbitrarily large, while the jump rates decay exponentially in the jump length and depend on the energy marks by a Boltzmann-like factor.
We will focus on the 1d case, recall some previous results on diffusivity and recurrence, and discuss more in detail the effect of applying an external uniform force field. We will give conditions assuring ballisticity or sub-ballisticity, which reduce to a full characterization in the case of a renewal simple point process.
