Antti Knowles

activity

20052026

most citedSpectral Statistics of Erd{\H o}s-Rényi Graphs II: Eigenvalue Spacing and the Extreme Eigenvalues

238 citations · 1.5k across the 41 of their papers we have counts for

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Showing 2021 · math.PRShow all

2 papers · 2 filters

math.PR2021

The completely delocalized region of the Erdős-Rényi graph

Johannes Alt, Raphael Ducatez, Antti Knowles

We analyse the eigenvectors of the adjacency matrix of the Erdős-Rényi graph on $N$ vertices with edge probability $\frac{d}{N}$ . We determine the full region of delocalization by…

math.PR2021★ 2 cited

Poisson statistics and localization at the spectral edge of sparse Erdős-Rényi graphs

Johannes Alt, Raphael Ducatez, Antti Knowles

We consider the adjacency matrix $A$ of the Erdős-Rényi graph on $N$ vertices with edge probability $d / N$ . For $(lo g lo g N)^{4} ≪ d ≲ lo g N$ , we prove that the eigenvalue…