On one generalization of the elliptic law for random matrices

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.

40 pages. arXiv admin note: text overlap with arXiv:1012.2710

References in corpus (4)

• On the Asymptotic Spectrum of Products of Independent Random Matrices
• Products of independent elliptic random matrices
• Elliptic law for real random matrices
• Circular law, Extreme Singular values and Potential theory

Cited by in corpus (4)

• Products of independent elliptic random matrices
• Products of Independent Gaussian Random Matrices
• Dynamical systems on large networks with predator-prey interactions are stable and exhibit oscillations
• Circular Law for Random Block Band Matrices with Genuinely Sublinear Bandwidth