The distribution of Lyapunov exponents: Exact results for random matrices

Research output: Contribution to journalArticle

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

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Exact Results
Random Matrices
Lyapunov Exponent
exponents
entry
Exponent
Product Integral
Stochastic Dynamical Systems
Linear Dynamical Systems
Wiener Process
products
Exponential distribution
Uniform distribution
dynamical systems
Zero
matrices

ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Physics and Astronomy(all)
  • Mathematical Physics

Cite this

The distribution of Lyapunov exponents : Exact results for random matrices. / Newman, Charles M.

In: Communications in Mathematical Physics, Vol. 103, No. 1, 03.1986, p. 121-126.

Research output: Contribution to journalArticle

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