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.
This is a preview of subscription content, log in to check access.
Buy single article
Instant access to the full article PDF.
Price includes VAT for USA
Subscribe to journal
Immediate online access to all issues from 2019. Subscription will auto renew annually.
This is the net price. Taxes to be calculated in checkout.
Received: 3 April 1995 / In revised form: 14 December 1996
About this article
Cite this article
Arous, G., Guionnet, A. Large deviations for Wigner's law and Voiculescu's non-commutative entropy. Probab Theory Relat Fields 108, 517–542 (1997). https://doi.org/10.1007/s004400050119
- Mathematics Subject of Classification: 60F10