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Large deviations for Wigner’s law and Voiculescu’s non-commutative entropy. (English) Zbl 0954.60029
Summary: We study the spectral measure of Gaussian Wigner’s matrices and prove that it satisfies a large deviation principle. We show that the good rate function which governs this principle achieves its minimum value at Wigner’s semicircular law, which entails the convergence of the spectral measure to the semicircular law. As a conclusion, we give some further examples of random matrices with spectral measure satisfying a large deviation principle and argue about Voiculescu’s non-commutative entropy.

MSC:
60F10 Large deviations
15A18 Eigenvalues, singular values, and eigenvectors
15B52 Random matrices (algebraic aspects)
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