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- W2145645384 abstract "For 0 β*, they grow exponentially. By formulating the problem as a Markov chain involving random matrix products and computing its invariant measure (a fractal) the Lyapunov constant σ(β) = limn→ ∞ | x n|1/n is determined numerically for a wide range of values β, and its dependence on β is observed to be non-smooth. (The limit is defined in the almost sure sense.) This generalizes recent work of Viswanath, who proved σ (1) = 1.131 988 24.... By a simple rescaling, these results also apply to the more general random recurrence x n+1 = α x n± β x n−1 for fixed α and β. These random recurrence relations have links with many fields, including ergodic theory, dynamical systems, heavy–tailed statistics, spectral theory, continued fractions, and condensed matter physics." @default.
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- W2145645384 date "1999-07-08" @default.
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- W2145645384 title "Growth and decay of random Fibonacci sequences" @default.
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