Random Matrices: Law of the Determinant
نویسنده
چکیده
Let An 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 | detAn| satisfies a central limit theorem. More precisely, sup x∈R ̨̨̨ P ` log(| detAn|)− 12 log(n− 1)! q 1 2 logn ≤ x ́ − Φ(x) ̨̨̨ ≤ log 1 3+o(1) n.
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