Abstract: It is a classic result in spectral theory that the limit distribution of the spectral measure of random graphs $G(n,p)$ converges to the semicircle law in case $np$ tends to infinity with $n$. A popular proof relies on the so called moment method where one shows that the 2k-th moment of the spectral distribution converges to the number of contour walks of trees of size k. The spectral measure for random graphs $G(n,c/n)$ however is less understood. In this work, we combine and extend two combinatorial approaches by Bauer and Golinelli (2001) and Enriquez and Menard (2016) and approximate the moments of the spectral measure by counting exhaustive walks on trees while stumbling upon interesting identities involving the Catalan generating function.
This is joint work with Elie de Panafieu.
Exhaustive tree walks and the spectrum of random graphs
18.04.2023 15:15 - 16:45
Organiser:
M. Drmota
Location: