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Bernoulli products of matrices: A deterministic model

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Abstract

The structure of the product of random matrices appearing as transfer matrices in several physical problems is studied. Making use of the fact that such matrices can be diagonalized by commuting matrices, we develop a graphical trick in order to control the properties of the product. The emergence of resonances gives a hint of the appearance of fluctuations and leads to a control of their amplitudes. We introduce a deterministic model (Tower model) reproducing the asymptotic random behaviour of the Bernoulli trials of such matrices. In particular the model is tested in computing Lyapunov exponents.

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Authors and Affiliations

  1. Centre de Physique Théorique, CNRS-Luminy, Case 907, F-13288, Marseille Cedex, France

    Ricardo Lima & Paola Piccoli

Authors
  1. Ricardo Lima
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  2. Paola Piccoli
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Additional information

Partially supported by BIBOS-Bielefeld-Bochum-Stochastic

Supported by fellowship of the ISAS (International School for Advanced Studies). Strada Costiera 11-TRIESTE-Italy

Laboratoire Propre N. 7061, Centre National de la Recherche Scientifique

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Lima, R., Piccoli, P. Bernoulli products of matrices: A deterministic model. Japan J. Appl. Math. 7, 515–526 (1990). https://doi.org/10.1007/BF03167857

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  • DOI: https://doi.org/10.1007/BF03167857

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