The randomly oriented graph $G_{ n,p}^{ \sigma}$ is an Erd\H{ o}s-R\'enyi 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 $n\rightarrow\infty$. It is worth mentioning that our result does not require finite moments of the entries of the underlying random matrix.
Categories: math.CO