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arXiv · 1111.6300

A central limit theorem for the determinant of a Wigner matrix

Terence Tao·Van Vu
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Abstract

We establish a central limit theorem for the log-determinant $\log|\det(M_n)|$ of a Wigner matrix $M_n$, under the assumption of four matching moments with either the GUE or GOE ensemble. More specifically, we show that this log-determinant is asymptotically distributed like $N(\log \sqrt{n!} - 1/2 \log n, 1/2 \log n)_\R$ when one matches moments with GUE, and $N(\log \sqrt{n!} - 1/4 \log n, 1/4 \log n)_\R$ when one matches moments with GOE.

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Terence Tao, Van Vu. 2011-11-27. A central limit theorem for the determinant of a Wigner matrix. https://arxiv.org/abs/1111.6300

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