Displaying similar documents to “Domains of analytic continuation for the top Lyapunov exponent”

Infinite products of random matrices and repeated interaction dynamics

Laurent Bruneau, Alain Joye, Marco Merkli (2010)

Annales de l'I.H.P. Probabilités et statistiques

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Let be a product of independent, identically distributed random matrices , with the properties that is bounded in , and that has a deterministic (constant) invariant vector. Assume that the probability of having only the simple eigenvalue 1 on the unit circle does not vanish. We show that is the sum of a fluctuating and a decaying process. The latter converges to zero almost surely, exponentially fast as →∞. The fluctuating part converges...

One-dimensional finite range random walk in random medium and invariant measure equation

Julien Brémont (2009)

Annales de l'I.H.P. Probabilités et statistiques

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We consider a model of random walks on ℤ with finite range in a stationary and ergodic random environment. We first provide a fine analysis of the geometrical properties of the central left and right Lyapunov eigenvectors of the random matrix naturally associated with the random walk, highlighting the mechanism of the model. This allows us to formulate a criterion for the existence of the absolutely continuous invariant measure for the environments seen from the particle. We then deduce...