A claimed optimal Berry-Esseen bound of order sqrt(d) N^{-1/6+eps} for eigenvector projections of random d-regular graphs, with a matching lower bound.
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Sharp Square Root Bounds for Edge Eigenvector Universality in Sparse Random Regular Graphs
A claimed optimal Berry-Esseen bound of order sqrt(d) N^{-1/6+eps} for eigenvector projections of random d-regular graphs, with a matching lower bound.