• Corpus ID: 119160069

Elliptic law for real random matrices

  title={Elliptic law for real random matrices},
  author={Alexey Naumov},
  journal={arXiv: Probability},
  • A. Naumov
  • Published 8 January 2012
  • Mathematics
  • arXiv: Probability
In this paper we consider ensemble of random matrices $\X_n$ with independent identically distributed vectors $(X_{ij}, X_{ji})_{i \neq j}$ 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… 

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