Power law scaling of the top Lyapunov exponent of a product of random matrices
A sequence of i.i.d. matrix-valued random variables /X/sub n// x X/sub n/ = (/sub 0//sup 1/ /sub 1//sup d/) with probability p and X/sub n/ = (/sub c(var epsilon)//sup 1 + a(var epsilon)/ /sub 1 + a(var epsilon)//sup b(var epsilon)/) with probability 1 - p is considered. Let a(var epsilon) = a/sub 0/ var epsilon + o(var epsilon) = c/sub 0/ var epsilon + o(var epsilon) lim/sub var epsilon ..-->.. 0/ b(var epsilon) = 0, a/sub 0/, c/sub 0/, var epsilon > 0, and b(var epsilon) > 0 for all var epsilon > 0. It is shown that the top Lyapunov exponent of the matrix product X/sub n/X/sub n-1/... X/sub 1/, lambda = lim/sub n ..-->.. infinity/ (1/n)/n perpendicular to X/sub n/X/sub n-1/... X/sub i/ satisfies a power law with an exponent 1/2. That is, lim/sub var epsilon ..-->.. 0/(1n lambda/1n var epsilon) = 1/2.
- Research Organization:
- State Univ. of New York, New Paltz (USA)
- OSTI ID:
- 6356992
- Journal Information:
- J. Stat. Phys.; (United States), Vol. 54:1-2
- Country of Publication:
- United States
- Language:
- English
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