Large deviations for Wigner's law and Voiculescu's non-commutative entropy
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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.
- Large deviations for Wigner's law and Voiculescu's non-commutative entropy
Probability Theory and Related Fields
Volume 108, Issue 4 , pp 517-542
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- Mathematics Subject of Classification: 60F10
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