Antti Knowles

Bernoulli flow for Erd\H{o}s-R\'enyi graphs

We study the eigenvalues and eigenvectors of the adjacency matrix $A$ of the Erd\H{o}s-R\'enyi graph $\mathbb G(N,p)$ in the regime $Np \gg (\log N)^2$. We establish optimal isotropic delocalization for the bulk eigenvectors $\boldsymbol u$, meaning that $\langle \boldsymbol v, \boldsymbol u\rangle^2 \leq \frac{C \log...