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math.PR2025
A semicircle law for the normalized Laplacian of sparse random graphs
Yiming Chen, Zijun Chen, Yizhe Zhu
We study the limiting spectral distribution of the normalized Laplacian of an Erdős-Rényi graph . To account for the presence of isolated vertices in the spars…
math.PR2024
Central limit theorems for linear spectral statistics of inhomogeneous random graphs with graphon limits
Xiangyi Zhu, Yizhe Zhu
We establish central limit theorems (CLTs) for the linear spectral statistics of the adjacency matrix of inhomogeneous random graphs across all sparsity regimes, providing explicit…
math.PR2023
Non-backtracking eigenvalues and eigenvectors of random regular graphs and hypergraphs
Xiangyi Zhu, Yizhe Zhu
The non-backtracking operator of a graph is a powerful tool in spectral graph theory and random matrix theory. Most existing results for the non-backtracking operator of a random g…