Abstract
We establish a moderate deviations principle (MDP) for the log-determinant log | det(M n ) | of a Wigner matrix M n matching four moments with either the GUE or GOE ensemble. Further we establish Cramér-type moderate deviations and Berry-Esseen bounds for the log-determinant for the GUE and GOE ensembles as well as for non-symmetric and non-Hermitian Gaussian random matrices (Ginibre ensembles), respectively.
2010 Mathematics Subject Classification. Primary 60B20; Secondary 60F10, 15A18
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The second author has been supported by Deutsche Forschungsgemeinschaft via SFB/TR 12.
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Dedicated to Friedrich Götze on the occasion of his sixtieth birthday
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Döring, H., Eichelsbacher, P. (2013). Moderate Deviations for the Determinant of Wigner Matrices. In: Eichelsbacher, P., Elsner, G., Kösters, H., Löwe, M., Merkl, F., Rolles, S. (eds) Limit Theorems in Probability, Statistics and Number Theory. Springer Proceedings in Mathematics & Statistics, vol 42. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-36068-8_12
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