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The Lyapunov spectrum of a continuous product of random matrices

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Abstract

We present a functional integration method for the averaging of continuous productsP t ofN×N random matrices. As an application, we compute exactly the statistics of the Lyapunov spectrum ofP t . This problem is relevant to the study of the statistical properties of various disordered physical systems, and specifically to the computation of the multipoint correlators of a passive scalar advected by a random velocity field. Apart from these applications, our method provides a general setting for computing statistical properties of linear evolutionary systems subjected to a white-noise force field.

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Authors and Affiliations

  1. Dipartimento di Matematica, Politecnico di Torino, 10129, Turin, Italy

    Andrea Gamba

  2. INFN, Sezione di Milano, 20133, Milan, Italy

    Andrea Gamba

  3. Budker Institute of Nuclear Physics, 630090, Novosibirsk, Russia

    Igor V. Kolokolov

Authors
  1. Andrea Gamba
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  2. Igor V. Kolokolov
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Communicated by J. L. Lebowitz

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Gamba, A., Kolokolov, I.V. The Lyapunov spectrum of a continuous product of random matrices. J Stat Phys 85, 489–499 (1996). https://doi.org/10.1007/BF02174216

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  • DOI: https://doi.org/10.1007/BF02174216

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