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 2020 · math.PRShow all

2 papers · 2 filters

math.PR2020

Delocalization transition for critical Erdős-Rényi graphs

Johannes Alt, Raphael Ducatez, Antti Knowles

We analyse the eigenvectors of the adjacency matrix of a critical Erdős-Rényi graph $G (N, d / N)$ , where $d$ is of order $lo g N$ . We show that its spectrum splits into two ph…

math.PR2020★ 2 cited

Fluctuations of extreme eigenvalues of sparse Erdős-Rényi graphs

Yukun He, Antti Knowles

We consider a class of sparse random matrices which includes the adjacency matrix of the Erdős-Rényi graph $G (N, p)$ . We show that if $N^{\varepsilon} \leq Np \leq N^{1/3-…