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We consider the rates of convergence of the quenched central limit theoremfor hitting times of one-dimensional random walks in a random environment.Previous results had identified polynomial upper bounds for the rates of decaywhich are sometimes slower than $n^{-1/2}$ (the optimal rate in the classicalBerry-Esseen estimates). Here we prove that the previous upper bounds are infact the best possible polynomial rates for the quenched CLT.

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