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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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math.PR2026

Density of states of randomly sprinkled graphs

Antti Knowles, Steffen Polzer

Independently at every vertex of a large core graph , we draw a random graph and connect to a subset of its vertices. This model of a randomly sprinkled graph ca…

math.PR2026

Bernoulli flow for Erdős-Rényi graphs

Joscha Henheik, Antti Knowles

We study the eigenvalues and eigenvectors of the adjacency matrix of the Erdős-Rényi graph in the regime . We establish optimal isotropic de…

math.PR2026

Semilocalization for inhomogeneous random graphs

Thomas Buc-d'Alché, Antti Knowles

We analyse the eigenvectors of the adjacency matrix of a random inhomogeneous graph constructed from a specified degree sequence. We assume that the empirical degree sequence has b…