Non-random perturbations of the Anderson Hamiltonian

Random Perturbations of 2-dimensional Hamiltonian Flows

We consider the motion of a particle in a periodic two dimensional flow perturbed by small (molecular) diffusion. The flow is generated by a divergence free zero mean vector field. The long time behavior corresponds to the behavior of the homogenized process that is diffusion process with the constant diffusion matrix (effective diffusivity). We obtain the asymptotics of the effective diffusivi...

Random Projection-Based Anderson-Darling Test for Random Fields

In this paper, we present the Anderson-Darling (AD) and Kolmogorov-Smirnov (KS) goodness of fit statistics for stationary and non-stationary random fields. Namely, we adopt an easy-to-apply method based on a random projection of a Hilbert-valued random field onto the real line R, and then, applying the well-known AD and KS goodness of fit tests. We conclude this paper by studying the behavior o...

Random perturbations of non - uniformly expanding maps ∗

We give both sufficient conditions and necessary conditions for the stochastic stability of non-uniformly expanding maps either with or without critical sets. We also show that the number of probability measures describing the statistical asymptotic behaviour of random orbits is bounded by the number of SRB measures if the noise level is small enough. As an application of these results we prove...

Random Perturbations of Non-Uniformly Expanding Maps

Splitting of the Landau Levels by Magnetic Perturbations and Anderson Transition in 2d-random Magnetic Media

In this note we consider a Landau Hamiltonian perturbed by a random magnetic potential of Anderson type. For a given number of bands, we prove the existence of both strongly localized states at the edges of the spectrum and dynamical delocalization near the center of the bands in the sense that wave packets travel at least at a given minimum speed. We provide explicit examples of magnetic pertu...