Empirical spectral distributions of arbitrary-degree polynomials in Ginibre matrices converge to their Brown measures as matrix size tends to infinity.
Circular law for non-Hermitian block band matrices with slowly growing bandwidth
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The second correlation function of characteristic polynomials for non-Hermitian random band matrices is studied asymptotically in the critical regime W proportional to sqrt(N) as N and W tend to infinity.
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Brown measure convergence for the spectrum of polynomials in Ginibre matrices
Empirical spectral distributions of arbitrary-degree polynomials in Ginibre matrices converge to their Brown measures as matrix size tends to infinity.
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Characteristic polynomials of non-Hermitian random band matrices near the threshold
The second correlation function of characteristic polynomials for non-Hermitian random band matrices is studied asymptotically in the critical regime W proportional to sqrt(N) as N and W tend to infinity.