Journal of Statistical Physics

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

Infinite Products of Random Isotropically Distributed Matrices



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.


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



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


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© 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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