Journal of Theoretical Probability

, Volume 23, Issue 2, pp 447–465 | Cite as

A Matrix Interpolation between Classical and Free Max Operations. I. The Univariate Case

  • Florent Benaych-Georges
  • Thierry Cabanal-Duvillard


Recently, Ben Arous and Voiculescu considered taking the maximum of two free random variables and brought to light a deep analogy with the operation of taking the maximum of two independent random variables. We present here a new insight on this analogy: its concrete realization based on random matrices giving an interpolation between classical and free settings.


Random matrices Free probability Max-stable laws 

Mathematics Subject Classification (2000)

15A52 46L54 


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Copyright information

© Springer Science+Business Media, LLC 2009

Authors and Affiliations

  • Florent Benaych-Georges
    • 1
    • 2
  • Thierry Cabanal-Duvillard
    • 3
  1. 1.LPMAUPMC Univ. Paris 6Paris Cedex 05France
  2. 2.CMAPÉcole PolytechniquePalaiseau CedexFrance
  3. 3.MAP 5UMR CNRS 8145–Université Paris DescartesParis cedex 6France

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