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Large deviations for Wigner's law and Voiculescu's non-commutative entropy
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  • Published: August 1997

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

  • G. Ben Arous1 &
  • A. Guionnet2 

Probability Theory and Related Fields volume 108, pages 517–542 (1997)Cite this article

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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.

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Authors and Affiliations

  1. URA 762, CNRS, DMI, Ecole Normale Superieure, F-75230 Paris, France, , , , , , FR

    G. Ben Arous

  2. URA 743, CNRS, Bat. 425, Université de Paris Sud, F-91405 Orsay, France, , , , , , FR

    A. Guionnet

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  1. G. Ben Arous
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  2. A. Guionnet
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Received: 3 April 1995 / In revised form: 14 December 1996

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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

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  • Issue Date: August 1997

  • DOI: https://doi.org/10.1007/s004400050119

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