Optimal quenched CLT rates of convergence

Sung Won Ahn, J. Peterson

2022, v.28, Issue 2, 215-244


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.

Keywords: quenched central limit theorem, rates of convergence


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