Random Walks in Fluctuating Random Media

#### M.S. Bernabei, C. Boldrighini

1996, v.2, №3, 401-426

ABSTRACT

We consider a discrete-time random walk on the lattice $Z^{\nu}$, in mutual interaction with a fluctuating random environment. We extend previous results on the validity of the Central Limit Theorem for the displacement of the random walk. Theorem 2.1 shows that we can remove the condition of strict locality if the interaction is small. Theorem 2.2 shows that in a particular case with strict locality the condition that the interaction can be replaced by a general nondegeneracy condition.

Keywords: random walk,random environment,diffusion,Central Limit Theorem