Tóth László Márton (Rényi Alfréd Matematikai Kutatóintézet): Friedman's second largest eigenvalue theorem for irregular random graphs

In 2008 Friedman showed that random d-regular graphs are almost Ramanujan, meaning that asymptotically they have the largest possible spectral gap among d-regular graphs.

We are able to extend this to irregular graphs with fixed degree distribution sampled with the configuration model. In order to achieve this we need to generalize a spectral result of Backhausz, Szegedy and Virág from regular trees to Unimodular Galton-Watson trees.

Ongoing joint work with Charles Bordenave.