Evolution of a passive particle in a one-dimensional diffusive environment (Q2685139)

The goal of this paper is to consider the fluctuations of a walker in an unbiased, one-dimensional, diffusive random environment, and to study different behaviors that may be observed depending on the time scales that the authors look at, providing insight for the resolution of the mentioned in the paper paradoxical conjectures. Two main results are obtained in the paper: 1) in the short time limit, it is shown that the fluctuations of the particle become Gaussian and sub-diffusive, with dynamical exponent 3/4; 2) in the long time limit, it is shown that the particle is trapped by the local minima of the potential and evolves diffusively i.e. with exponent 1/2.