Uniform regular weighted graphs with large degree: Wigner's law, asymptotic freeness and graphons limit

Camille Male, Sandrine Péché

For each $N\ge 1$, let $G_N$ be a simple random graph on the set of vertices $[N]=\{1,2,...,N\}$, which is invariant by relabeling of the vertices. The asymptotic behavior as $N…