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arXiv · 1404.7013

On one generalization of the elliptic law for random matrices

Friedrich Götze·Alexey Naumov·Alexander Tikhomirov
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Abstract

We consider the products of $m\ge 2$ independent large real random matrices with independent vectors $(X_{jk}^{(q)},X_{kj}^{(q)})$ of entries. The entries $X_{jk}^{(q)},X_{kj}^{(q)}$ are correlated with $\rho=\mathbb E X_{jk}^{(q)}X_{kj}^{(q)}$. The limit distribution of the empirical spectral distribution of the eigenvalues of such products doesn't depend on $\rho$ and equals to the distribution of $m$th power of the random variable uniformly distributed on the unit disc.

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Friedrich Götze, Alexey Naumov, Alexander Tikhomirov. 2014-04-28. On one generalization of the elliptic law for random matrices. https://doi.org/10.5506/aphyspolb.46.1737

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