Yukun He

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math.PR2025

Gaussian Waves and Edge Eigenvectors of Random Regular Graphs

Yukun He, Jiaoyang Huang, Horng-Tzer Yau

Backhausz and Szegedy (2019) demonstrated that the almost eigenvectors of random regular graphs converge to Gaussian waves with variance $0 \leq σ^{2} \leq 1$ . In this paper, we presen…

math.PR2019

Bulk eigenvalue fluctuations of sparse random matrices

Yukun He

We consider a class of sparse random matrices, which includes the adjacency matrix of Erdős-Rényi graphs $G (N, p)$ for $p \in [N^{ε - 1}, N^{- ε}]$ . We iden…