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

Sung Won Ahn; Jonathon Peterson

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arXiv · 2001.11522

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

Sung Won Ahn·Jonathon Peterson

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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.

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BibTeX RIS

Sung Won Ahn, Jonathon Peterson. 2020-01-30. Optimal rates of convergence for quenched central limit theorem rates for hitting times of one-dimensional random walks in random environments. https://arxiv.org/abs/2001.11522

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