Optimal rates of convergence for quenched central limit theorem rates for hitting times of one-dimensional random walks in random environments

Abstract

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.

22 pages; changed title

References in corpus (3)

• Quenched limits for transient, zero speed one-dimensional random walk in random environment
• Limiting distributions and large deviations for random walks in random environments
• On slowdown and speedup of transient random walks in random environment