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Rapport Année : 2000

Series Expansions of Lyapunov Exponents and Forgetful Monoids

Résumé

We consider Lyapunov exponents of random iterates of monotone homogeneous maps. We assume that the images of some iterates are lines, with positive probability. Using this memory-loss property which holds generically for random products of matrices over the max-plus semiring, and in particular, for Tetris-like heaps of pieces models, we give a series expansion formula for the Lyapunov exponent, as a function of the probability law. In the case of rational probability laws, we show that the Lyapunov exponent is an analytic function of the parameters of the law, in a domain that contains the absolute convergence domain of a partition function associated to a special «forgetful» monoid, defined by generators and relations.
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Dates et versions

inria-00072677 , version 1 (24-05-2006)

Identifiants

  • HAL Id : inria-00072677 , version 1

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Stéphane Gaubert, Dohy Hong. Series Expansions of Lyapunov Exponents and Forgetful Monoids. RR-3971, INRIA. 2000. ⟨inria-00072677⟩
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