Author

Jiao-Yang Huang

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Preprint Sep 2026

The oriented Kesten--McKay law for random regular digraphs

We consider the adjacency matrix of a random directed $d$-regular graph on $N$ vertices. For fixed $d\geq 2$, we prove that the empirical eigenvalue density converges in probability to the oriented Kesten--McKay law as $N\to \infty$. The key technical input is the small-ball probability estimate for the smallest singul...

Yu-Kun He, Jiao-Yang Huang · 1 citation

Preprint Oct 2026

Bulk universality of random regular graphs

We consider the adjacency matrix of a uniformly random simple $d$-regular graph on $N$ vertices. For every fixed $d\geq3$ and every fixed bulk energy, we prove that the rescaled eigenvalue point process converges to the $\mathrm{Sine}_1$ process with intensity $1/\pi$. We also establish universality of consecutive gaps...

Yu-Kun He, Jiao-Yang Huang, Xiao-Yun Wang · 0 citations