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

Abstract

We present a functional integration method for the averaging of continuous productsPt ofN×N random matrices. As an application, we compute exactly the statistics of the Lyapunov spectrum ofPt. 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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