Limiting velocity of high-dimensional random walk in random environment

On the Limiting Velocity of High-dimensional Random Walk in Random Environment

We show that Random Walk in uniformly elliptic i.i.d. environment in dimension ≥ 5 has at most one non-zero limiting velocity. In particular this proves a law of large numbers in the distributionally symmetric case and establishes connections between different conjectures.

Weak Quenched Limiting Distributions for Transient One-dimensional Random Walk in a Random Environment

We consider a one-dimensional, transient random walk in a random i.i.d. environment. The asymptotic behaviour of such random walk depends to a large extent on a crucial parameter κ > 0 that determines the fluctuations of the process. When 0 < κ < 2, the averaged distributions of the hitting times of the random walk converge to a κ-stable distribution. However, it was shown recently that in this...

Tail estimates for one-dimensional random walk in random environment

Suppose that the integers are assigned i.i.d. random variables f! x g (taking values in the unit interval), which serve as an environment. This environment deenes a random walk fX k g (called a RWRE) which, when at x, moves one step to the right with probability ! x , and one step to the left with probability 1 ? ! x. Solomon (1975) determined the almost-sure asymptotic speed (=rate of escape) ...

Random walk on a two-dimensional random environment

Random Walk in a Random Multiplieative Environment

We investigate the dynamics of a random walk in a random multiplicative medium. This results in a random, but correlated, multiplicative process for the spatial distribution of random walkers. We show how the details of these correlations determine the asymptotic properties of the walk, i.e., the central limit theorem does not apply to these multiplicative processes. We also study a periodic so...