Asymptotic behavior for log-determinants of several non-Hermitian random matrices

Abstract

We study the asymptotic behavior for log-determinants of two unitary but non-Hermitian random matrices: the spherical ensembles A⁻¹B, where A and B are independent complex Ginibre ensembles and the truncation of circular unitary ensembles. The corresponding Berry-Esseen bounds and Cramér type moderate deviations are established. Our method is based on the estimates of corresponding cumulants. Numerical simulations are also presented to illustrate the theoretical results.

Keywords

Log-determinants / Berry-Esseen bounds / moderate deviations / spherical ensembles / circular unitary ensembles

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Higher Education Press and Springer-Verlag Berlin Heidelberg