The distribution of Lyapunov exponents: Exact results for random matrices

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Abstract

Simple exact expressions are derived for all the Lyapunov exponents of certain N-dimensional stochastic linear dynamical systems. In the case of the product of independent random matrices, each of which has independent Gaussian entries with mean zero and variance 1/N, the exponents have an exponential distribution as N→∞. In the case of the time-ordered product integral of exp[N-1/2dW], where the entries of the N×N matrix W(t) are independent standard Wiener processes, the exponents are equally spaced for fixed N and thus have a uniform distribution as N→∞.

Original languageEnglish (US)
Pages (from-to)121-126
Number of pages6
JournalCommunications In Mathematical Physics
Volume103
Issue number1
DOIs
StatePublished - Mar 1986

ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Mathematical Physics

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