Almost-Sure Central Limit Theorem for a Model of Random Walk in Fluctuating Random Environment

#### M.S. Bernabei, C. Boldrighini, R.A. Minlos, A. Pellegrinotti

1998, v.4, №3, 381-393

ABSTRACT

The Central Limit Theorem (CLT) for a class of discrete-time random walks on the lattice $Z^\nu$, $\nu\geq 2$, in a fluctuating random environment was proved in [C. Boldrighini, R.A. Minlos and A. Pellegrinotti, Almost-sure central limit theorem for a Markov model of random walk in dynamical random environment, Probab. Theory and Relat. Fields, 1997, 109, 245-273] for almost all realizations of the space-time environment. In the present paper we extend the result to the case $\nu=1$. The proof is based on the moment method and can be extended to all dimensions $\nu\geq 1$.

Keywords: random walk,random environment,central limit theorem