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Edge Universality of Random Regular Graphs of Growing Degrees

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arxiv 2305.01428 v2 pith:XMV2TUG2 submitted 2023-05-02 math.PR math.CO

Jiaoyang Huang , Horng-Tzer Yau This is my paper · ORCID
classification math.PRmath.CO
keywords eigenvaluesgraphsmathfrakregularextremerandomabsolutearbitrarily
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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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Cited by 2 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. Quantitative Edge Eigenvector Universality for Random Regular Graphs: Berry-Esseen Bounds with Explicit Constants

    math.PR 2025-07 reject novelty 7.0 of 10

    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.

  2. Gaussian Waves and Edge Eigenvectors of Random Regular Graphs

    math.PR 2025-02 conditional novelty 6.0 of 10

    Edge eigenvectors of random d-regular graphs converge to Gaussian waves with variance 1, jointly with and asymptotically independent of the Airy_1 edge eigenvalue process.

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