  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.
