Ballistic Random Walks in Random Environment at Low Disorder

Sharp ellipticity conditions for ballistic behavior of random walks in random environment

Random Dirichlet environment viewed from the particle in dimension d3

We consider random walks in random Dirichlet environment (RWDE), which is a special type of random walks in random environment where the exit probabilities at each site are i.i.d. Dirichlet random variables. On Z, RWDE are parameterized by a 2d-tuple of positive reals called weights. In this paper, we characterize for d≥ 3 the weights for which there exists an absolutely continuous invariant pr...

Ballistic Phase of Self-Interacting Random Walks

We explain a unified approach to a study of ballistic phase for a large family of self-interacting random walks with a drift and self-interacting polymers with an external stretching force. The approach is based on a recent version of the OrnsteinZernike theory developed in Campanino et al. (2003, 2004, 2007). It leads to local limit results for various observables (e.g., displacement of the en...

A PRELUDE TO THE THEORY OF RANDOM WALKS IN RANDOM ENVIRONMENTS

A random walk on a lattice is one of the most fundamental models in probability theory. When the random walk is inhomogenous and its inhomogeniety comes from an ergodic stationary process, the walk is called a random walk in a random environment (RWRE). The basic questions such as the law of large numbers (LLN), the central limit theorem (CLT), and the large deviation principle (LDP) are ...

Gaussian fluctuations for random walks in random mixing environments

We consider a class of ballistic, multidimensional random walks in random environments where the environment satisfies appropriate mixing conditions. Continuing our previous work [2] for the law of large numbers, we prove here that the fluctuations are gaussian when the environment is Gibbsian satisfying the “strong mixing condition” of Dobrushin and Shlosman and the mixing rate is large enough...