Nonconvex homogenization for one-dimensional controlled random walks in random potential

A log-scale limit theorem for one-dimensional random walks in random environments

We consider a transient one-dimensional random walk Xn in random environment having zero asymptotic speed. For a class of non-i.i.d. environments we show that log Xn/ log n converges in probability to a positive constant. MSC2000: primary 60K37, 60F05; secondary 60F10, 60J85.

Log-periodic modulation in one-dimensional random walks

We have studied the diffusion of a single particle on a one-dimensional lattice. It is shown that, for a self-similar distribution of hopping rates, the time dependence of the mean-square displacement follows an anomalous power law modulated by logarithmic periodic oscillations. The origin of this modulation is traced to the dependence on the length of the diffusion coefficient. Both the random...

Limit theorems for one and two-dimensional random walks in random scenery

One-dimensional discrete-time quantum walks on random environments

We consider discrete-time nearest-neighbor quantum walks on random environments in one dimension. Using the method based on a path counting, we present both quenched and annealed weak limit theorems for the quantum walk.

Level Crossing Probabilities I: One-dimensional Random Walks and Symmetrization

Abstract. We prove for an arbitrary one-dimensional random walk with independent increments that the probability of crossing a level at a given time n is O(n). Moment or symmetry assumptions are not necessary. In removing symmetry the (sharp) inequality P (|X+Y | ≤ 1) < 2P (|X−Y | ≤ 1) for independent identically distributed X, Y is used. In part II we shall discuss the connection of this resul...