A limit theorem for the position of a particle in the Lorentz model.
Ageing in the parabolic Anderson model
The parabolic Anderson model is the Cauchy problem for the heat equation with a random potential. We consider this model in a setting which is continuous in time and discrete in space, and focus on time-constant, independent and identically distributed potentials with polynomial tails at infinity. We are concerned with the long-term temporal dynamics of this system. Our main result is that the periods, in which the profile of the solutions remains nearly constant, are increasing linearly over time,...
Anomalous quantum transport in presence of self-similar spectra
Averaged large deviations for random walk in a random environment
In his 2003 paper, Varadhan proves the averaged large deviation principle for the mean velocity of a particle taking a nearest-neighbor random walk in a uniformly elliptic i.i.d. environment on ℤd with d≥1, and gives a variational formula for the corresponding rate function Ia. Under Sznitman’s transience condition (T), we show that Ia is strictly convex and analytic on a non-empty open set , and that the true velocity of the particle is an element (resp. in the boundary) of when the walk is non-nestling...