Unlike classical simple random walks, one-dimensional random walks in random environments (RWRE) are known to have a wide array of potential limiting distributions. Under certain assumptions, however, it is known that CLT-like limiting distributions hold for the walk under both the quenched and averaged measures. We give upper bounds on the rates of convergence for the quenched central limit theorems for both the hitting time and position of the RWRE with polynomial rates of convergence that depend on the distribution on environments.
"Quenched central limit theorem rates of convergence for one-dimensional random walks in random environments." Bernoulli 25 (2) 1386 - 1411, May 2019. https://doi.org/10.3150/18-BEJ1024