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The compound Poisson distribution and return times in dynamical systems
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  • Published: 12 April 2008

The compound Poisson distribution and return times in dynamical systems

  • Nicolai Haydn1 &
  • Sandro Vaienti2,3 

Probability Theory and Related Fields volume 144, pages 517–542 (2009)Cite this article

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Abstract

Previously it has been shown that some classes of mixing dynamical systems have limiting return times distributions that are almost everywhere Poissonian. Here we study the behaviour of return times at periodic points and show that the limiting distribution is a compound Poissonian distribution. We also derive error terms for the convergence to the limiting distribution. We also prove a very general theorem that can be used to establish compound Poisson distributions in many other settings.

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Author information

Authors and Affiliations

  1. Mathematics Department, University of Southern California, Los Angeles, CA, 90089-1113, USA

    Nicolai Haydn

  2. Centre de Physique Théorique, UMR 6207, CNRS, Luminy Case 907, 13288, Marseille Cedex 9, France

    Sandro Vaienti

  3. Universities of Aix-Marseille I, II and Toulon-Var, Fédération de Recherche des Unités de Mathématiques de Marseille, Marseille, France

    Sandro Vaienti

Authors
  1. Nicolai Haydn
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  2. Sandro Vaienti
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Corresponding author

Correspondence to Nicolai Haydn.

Additional information

This work was supported by a grant from the NSF (DMS-0301910) and by a grant from the Université de Toulon et du Var, France.

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Cite this article

Haydn, N., Vaienti, S. The compound Poisson distribution and return times in dynamical systems. Probab. Theory Relat. Fields 144, 517–542 (2009). https://doi.org/10.1007/s00440-008-0153-y

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  • Received: 21 March 2007

  • Revised: 04 March 2008

  • Published: 12 April 2008

  • Issue Date: July 2009

  • DOI: https://doi.org/10.1007/s00440-008-0153-y

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Mathematics Subject Classification (2000)

  • Primary: 37A50
  • Secondary: 62E17
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