Elliptic law for real random matrices

In this paper we consider ensemble of random matrices ${\text{X}}_n$ with independent identically distributed vectors $(X_{ij},X_{ji}{)}_{i\mathrm{\ne }j}$ of entries. Under assumption of finite fourth moment of matrix entries it is proved that empirical spectral distribution of eigenvalues converges in probability to a uniform distribution on the ellipse. The axis of the ellipse are determined by correlation between $X_{12}$ and $X_{21}$. This result is called Elliptic Law. Limit distribution doesn’t depend on distribution of matrix elements and the result in this sence is universal.