Probability Theory and Related Fields

, Volume 108, Issue 4, pp 517–542

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

  • G. Ben Arous
  • A. Guionnet

DOI: 10.1007/s004400050119

Cite this article as:
Arous, G. & Guionnet, A. Probab Theory Relat Fields (1997) 108: 517. doi:10.1007/s004400050119

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.

Mathematics Subject of Classification: 60F1015A1815A52

Copyright information

© Springer-Verlag Berlin Heidelberg 1997

Authors and Affiliations

  • G. Ben Arous
    • 1
  • A. Guionnet
    • 2
  1. 1.URA 762, CNRS, DMI, Ecole Normale Superieure, F-75230 Paris, FranceFR
  2. 2.URA 743, CNRS, Bat. 425, Université de Paris Sud, F-91405 Orsay, FranceFR