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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 vertices with edge probability . We determine the full region of delocalization by…
math.PR2021
Poisson statistics and localization at the spectral edge of sparse Erdős-Rényi graphs
Johannes Alt, Raphael Ducatez, Antti Knowles
We consider the adjacency matrix of the Erdős-Rényi graph on vertices with edge probability . For , we prove that the eigenvalue…
math.PR2021★ 1 cited
Local elliptic law
Johannes Alt, Torben Krüger
The empirical eigenvalue distribution of the elliptic random matrix ensemble tends to the uniform measure on an ellipse in the complex plane as its dimension tends to infinity. We…