A central limit theorem for the determinant of a Wigner matrix

Details A central limit theorem for the determinant of a Wigner matrix A central limit theorem for the determinant of a Wigner matrix

2011-11-27

arxiv.org/abs/1111.6300v3

Mathematics

Probability

29 pages, no figures, to appear, Adv. Math.. This is the final version

Scientific paper

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.

Affiliated with

Also associated with

No associations

Rating

A central limit theorem for the determinant of a Wigner matrix does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with A central limit theorem for the determinant of a Wigner matrix, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and A central limit theorem for the determinant of a Wigner matrix will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-66611