Optimal Rates of Convergence in Quenched Central Limit Theorem for Hitting Times of Random Walks in Random Environments

摘要

We consider the rates of convergence of the quenched central limit theorem for hitting times of one-dimensional random walks in a random environment. Previous results had identified polynomial upper bounds for the rates of decay which are sometimes slower than n~(-1/2) (the optimal rate in the classical Berry-Esseen estimates). Here we prove that the previous upper bounds are in fact the best possible polynomial rates for the quenched CLT.