Ben Arous, G.; Guionnet, A. Large deviations for Wigner’s law and Voiculescu’s non-commutative entropy. (English) Zbl 0954.60029 Probab. Theory Relat. Fields 108, No. 4, 517-542 (1997). 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. Cited in 1 ReviewCited in 145 Documents MSC: 60F10 Large deviations 15A18 Eigenvalues, singular values, and eigenvectors 15B52 Random matrices (algebraic aspects) Keywords:spectral measure; Gaussian Wigner’s matrices; large deviation principle; non-commutative entropy × Cite Format Result Cite Review PDF Full Text: DOI