On the skew-spectral distribution of randomly oriented graphs

The randomly oriented graph G(n,p)(sigma) is an ErdOs-Renyi random graph G(n,p) with a random orientation sigma, which assigns to each edge a direction so that G(n,p)(sigma) becomes a directed graph. Denote by S-n the skew-adjacency matrix of G(n,p)(sigma). Under some mild assumptions, it is proved in this paper that, the spectral distribution of S-n (under some normalization) converges to the standard semicircular law almost surely as n -> infinity. It is worth mentioning that our result does not require finite moments of the entries of the underlying random matrix.