Power law scaling of the top Lyapunov exponent of a Product of Random Matrices期刊界 All Journals 搜尽天下杂志传播学术成果专业期刊搜索期刊信息化学术搜索

Power law scaling of the top Lyapunov exponent of a Product of Random Matrices

Authors:	K. Ravishankar

Affiliation:	(1) Department of Mathematics and Computer Science, State University of New York, 12561 New Paltz, New York

Abstract:	A sequence of i.i.d. matrix-valued random variables $left{ {X_n } right} cdot X_n = left( {begin{array}{{20}c} 1 & d 0 & 1 end{array} } right)$ with probabilityp and $X_n = left( {begin{array}{{20}c} {1 + a(varepsilon )} & {b(varepsilon )} {c(varepsilon )} & {1 + a(varepsilon )} end{array} } right)$ with probability 1–p is considered. Leta() = a₀ + O(), c() = c₀ + O() lim₀b() = Oa₀,c₀, >0, andb()>0 for all >0. It is shown show that the top Lyapunov exponent of the matrix productX_nX_n-1...X₁, = lim_n (1/n) n X_nX_n-1...X₁ satisfies a power law with an exponent 1/2. That is, lim₀(ln /ln ) = 1/2.

Keywords:	Lyapunov exponent product of random matrices Markov chain
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