Asymptotic behavior for log-determinants of several non-Hermitian random matrices |
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Authors: | Lei Chen Shaochen Wang |
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Institution: | 1.School of Mathematics and Statistics,Jiangsu Normal University,Xuzhou,China;2.School of Mathematics,South China University of Technology,Guangzhou,China |
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Abstract: | We study the asymptotic behavior for log-determinants of two unitary but non-Hermitian random matrices: the spherical ensembles A -1 B; 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. |
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