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 2018 · math.PRShow all

2 papers · 2 filters

math.PR2018★ 1 cited

Local law and complete eigenvector delocalization for supercritical Erdős-Rényi graphs

Yukun He, Antti Knowles, Matteo Marcozzi

We prove a local law for the adjacency matrix of the Erdős-Rényi graph $G (N, p)$ in the supercritical regime $pN \geq C lo g N$ where $G (N, p)$ has with high probability no isolated…

math.PR2018★ 1 cited

Mesoscopic eigenvalue density correlations of Wigner matrices

Yukun He, Antti Knowles

We investigate to what extent the microscopic Wigner-Gaudin-Mehta-Dyson (WGMD) (or sine kernel) statistics of random matrix theory remain valid on mesoscopic scales. To that end, w…