Random matrices: Law of the determinant

Details Random matrices: Law of the determinant Random matrices: Law of the determinant

2011-12-04

arxiv.org/abs/1112.0752v2

Mathematics

Probability

Some trivial typos corrected, others to be updated soon

Scientific paper

Let $A_n$ be an $n$ by $n$ random matrix whose entries are independent real
random variables with mean zero and variance one. We show that the logarithm of
$|det A_n|$ satisfies a central limit theorem. More precisely,
$$\sup_{x\in R} |P(\frac{\log (|det A_n|)- 1/2 \log(n-1)!}{\sqrt{1/2 \log
n}}\le x) -\Phi(x)| \le \log^{-1/3 +o(1)} n.$$

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