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

collaborators

Showing 2015 · math.PRShow all

3 papers · 2 filters

math.PR2015

Eigenvalue confinement and spectral gap for random simplicial complexes

Antti Knowles, Ron Rosenthal

We consider the adjacency operator of the Linial-Meshulam model for random simplicial complexes on $n$ vertices, where each $d$ -cell is added independently with probability $p$ to…

math.PR2015★ 53 cited

Bulk eigenvalue statistics for random regular graphs

Roland Bauerschmidt, Jiaoyang Huang, Antti Knowles +1

We consider the uniform random $d$ -regular graph on $N$ vertices, with $d \in [N^{α}, N^{2/3 - α}]$ for arbitrary $α > 0$ . We prove that in the bulk of the spectrum the local eigenvalue…

math.PR2015★ 54 cited

Local semicircle law for random regular graphs

Roland Bauerschmidt, Antti Knowles, Horng-Tzer Yau

We consider random $d$ -regular graphs on $N$ vertices, with degree $d$ at least $(lo g N)^{4}$ . We prove that the Green's function of the adjacency matrix and the Stieltjes transform…