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Frontiers of Mathematics in China

Front. Math. China    2017, Vol. 12 Issue (4) : 805-819     DOI: 10.1007/s11464-017-0629-0
RESEARCH ARTICLE |
Asymptotic behavior for log-determinants of several non-Hermitian random matrices
Lei CHEN1,2, Shaochen WANG1,2()
1. School of Mathematics and Statistics, Jiangsu Normal University, Xuzhou 221116, China
2. School of Mathematics, South China University of Technology, Guangzhou 510640, 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−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     
Corresponding Authors: Shaochen WANG   
Issue Date: 06 July 2017
 Cite this article:   
Lei CHEN,Shaochen WANG. Asymptotic behavior for log-determinants of several non-Hermitian random matrices[J]. Front. Math. China, 2017, 12(4): 805-819.
 URL:  
http://journal.hep.com.cn/fmc/EN/10.1007/s11464-017-0629-0
http://journal.hep.com.cn/fmc/EN/Y2017/V12/I4/805
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Lei CHEN
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