Author

Antti Knowles

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Preprint Sep 2026

Density of states of randomly sprinkled graphs

Independently at every vertex $x$ of a large core graph $\mathbb G$, we draw a random graph and connect $x$ to a subset of its vertices. This model of a randomly sprinkled graph captures qualitative features of commonly observed graphs; it can also be regarded as a model of quantum disorder, where disorder arises from...

Antti Knowles, Steffen Polzer · 0 citations

Preprint Sep 2026

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...

Joscha Henheik, Antti Knowles · 0 citations