T^{-1/4}- noise for random walks in dynamic environment on Z.

We consider a discrete-time random walk in a random environment X_t on Z, whose transitions are small perturbations of a given kernel. The local environment takes finitely many values, and is i.i.d. distributed. It is known that when the perturbation term is small enough, a central limit theorem holds almost surely, and the dispersion is independent of the field. In this paper, the authors prove that the first correction term to this central limit theorem is of order T^{−1/4}, that it depends on the field, and that its distribution is asymptotically Gaussian when T tends to infinity.