Journal of Statistical Physics

, Volume 150, Issue 4, pp 678–703 | Cite as

Gaussian Multiplicative Chaos for Symmetric Isotropic Matrices

  • Laurent Chevillard
  • Rémi Rhodes
  • Vincent Vargas


Motivated by isotropic fully developed turbulence, we define a theory of symmetric matrix valued isotropic Gaussian multiplicative chaos. Our construction extends the scalar theory developed by J.P. Kahane in 1985.


Gaussian multiplicative chaos Random matrices Fully developed turbulence 



The authors wish to thank Krzysztof Gawȩdzki, Alice Guionnet and Raoul Robert for fruitful discussions, and grant ANR-11-JCJC CHAMU for financial support.


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Copyright information

© Springer Science+Business Media New York 2013

Authors and Affiliations

  • Laurent Chevillard
    • 1
  • Rémi Rhodes
    • 2
  • Vincent Vargas
    • 2
  1. 1.Laboratoire de Physique de l’ENS LyonCNRSLyon Cedex 07France
  2. 2.Ceremade, UMR 7564Université Paris-DauphineParis Cedex 16France

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