Advertisement

Springer Nature is making SARS-CoV-2 and COVID-19 research free. View research | View latest news | Sign up for updates

Large deviations for Wigner's law and Voiculescu's non-commutative entropy

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.

This is a preview of subscription content, log in to check access.

Author information

Additional information

Received: 3 April 1995 / In revised form: 14 December 1996

Rights and permissions

Reprints and Permissions

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

Download citation

  • Mathematics Subject of Classification: 60F10
  • 15A18
  • 15A52