Spectral Statistics of Sparse Random Graphs with a General Degree Distribution

Ben Adlam; Ziliang Che

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arXiv · 1509.03368

Spectral Statistics of Sparse Random Graphs with a General Degree Distribution

Ben Adlam·Ziliang Che

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Abstract

We consider the adjacency matrices of sparse random graphs from the Chung-Lu model, where edges are added independently between the $N$ vertices with varying probabilities $p_{ij}$. The rank of the matrix $(p_{ij})$ is some fixed positive integer. We prove that the distribution of eigenvalues is given by the solution of a functional self-consistent equation. We prove a local law down to the optimal scale and prove bulk universality. The results are parallel to \cite{Erdos2013b} and \cite{Landon2015}.

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Ben Adlam, Ziliang Che. 2015-09-11. Spectral Statistics of Sparse Random Graphs with a General Degree Distribution. https://arxiv.org/abs/1509.03368

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