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 2019 · math.PRShow all

2 papers · 2 filters

math.PR2019★ 31 cited

Edge rigidity and universality of random regular graphs of intermediate degree

Roland Bauerschmidt, Jiaoyang Huang, Antti Knowles +1

For random $d$ -regular graphs on $N$ vertices with $1 ≪ d ≪ N^{2/3}$ , we develop a $d^{- 1/2}$ expansion of the local eigenvalue distribution about the Kesten-McKay law up to or…

math.PR2019

Extremal eigenvalues of critical Erdős-Rényi graphs

Johannes Alt, Raphaël Ducatez, Antti Knowles

We complete the analysis of the extremal eigenvalues of the the adjacency matrix $A$ of the Erdős-Rényi graph $G (N, d / N)$ in the critical regime $d ≍ lo g N$ of the transition…