Journal of Statistical Physics

, Volume 85, Issue 3–4, pp 489–499 | Cite as

The Lyapunov spectrum of a continuous product of random matrices

  • Andrea Gamba
  • Igor V. Kolokolov
Short Communications


We present a functional integration method for the averaging of continuous productsP t ofN×N random matrices. As an application, we compute exactly the statistics of the Lyapunov spectrum ofP t . This problem is relevant to the study of the statistical properties of various disordered physical systems, and specifically to the computation of the multipoint correlators of a passive scalar advected by a random velocity field. Apart from these applications, our method provides a general setting for computing statistical properties of linear evolutionary systems subjected to a white-noise force field.

Key Words

Lyapunov exponents random matrices functional integral disordered systems passive scalar Gauss decomposition loop groups 


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Copyright information

© Plenum Publishing Corporation 1996

Authors and Affiliations

  • Andrea Gamba
    • 1
    • 2
  • Igor V. Kolokolov
    • 3
  1. 1.Dipartimento di MatematicaPolitecnico di TorinoTurinItaly
  2. 2.INFN, Sezione di MilanoMilanItaly
  3. 3.Budker Institute of Nuclear PhysicsNovosibirskRussia

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