The paper claims a quantitative Berry-Esseen bound for edge eigenvectors of random regular graphs, but the proof relies on an incorrect local law and contradicts itself on the rate.
Edge Universality of Random Regular Graphs of Growing Degrees
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abstract
We consider the statistics of extreme eigenvalues of random $d$-regular graphs, with $N^{\mathfrak c}\leq d\leq N^{1/3-{\mathfrak c}}$ for arbitrarily small ${\mathfrak c}>0$. We prove that in this regime, the fluctuations of extreme eigenvalues are given by the Tracy-Widom distribution. As a consequence, about 69% of $d$-regular graphs have all nontrivial eigenvalues bounded in absolute value by $2\sqrt{d-1}$.
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Quantitative Edge Eigenvector Universality for Random Regular Graphs: Berry-Esseen Bounds with Explicit Constants
The paper claims a quantitative Berry-Esseen bound for edge eigenvectors of random regular graphs, but the proof relies on an incorrect local law and contradicts itself on the rate.