Fluctuations of extreme eigenvalues of sparse Erdős-Rényi graphs

Yukun He, Antti Knowles

We consider a class of sparse random matrices which includes the adjacency matrix of the Erdős-Rényi graph $\mathcal{G}(N,p)$. We show that if $N^{\varepsilon} \leq Np \leq N^{1/3-…