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Journal of Statistical Physics

, Volume 166, Issue 1, pp 24–38 | Cite as

Infinite Products of Random Isotropically Distributed Matrices

  • A. S. Il’yn
  • V. A. Sirota
  • K. P. Zybin
Article

Abstract

Statistical properties of infinite products of random isotropically distributed matrices are investigated. Both for continuous processes with finite correlation time and discrete sequences of independent matrices, a formalism that allows to calculate easily the Lyapunov spectrum and generalized Lyapunov exponents is developed. This problem is of interest to probability theory, statistical characteristics of matrix T-exponentials are also needed for turbulent transport problems, dynamical chaos and other parts of statistical physics.

Keywords

Lyapunov exponents Random matrices T-exponential Functional integral Stochastic equations Turbulence Qft 

Notes

Acknowledgements

This work is supported by the RAS program ‘Nonlinear dynamics in mathematical and physical sciences’.

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Copyright information

© Springer Science+Business Media New York 2016

Authors and Affiliations

  1. 1.P.N.Lebedev Physical Institute of RASMoscowRussia
  2. 2.National Research University Higher School of EconomicsMoscowRussia

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