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Boltzmann-Gibbs Weights in the Branching Random Walk

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Classical and Modern Branching Processes

Part of the book series: The IMA Volumes in Mathematics and its Applications ((IMA,volume 84))

Abstract

Considering a branching random walk as a tree model for many physical disordered systems the a.s. convergence of the free energy is proved under minimal assumption (finite mean) on the partition function. The overlap of two nodes in the tree is their last common ancestor (or the common part of their branches). Under a “k log k-type” assumption the overlap of two nodes of height n picked up with Boltzmann-Gibbs weights is proved to have an explicit limit distribution. This extends a result of Joffe and simplify a proof of Derrida and Spohn.

AMS(MOS) subject classifications. Primary: 60J80, 60K35. Secondary: 60F10, 82C41.

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Author information

Authors and Affiliations

  1. Departement de Mathematiques, Universite de Versailles Saint Quentin, 45 Avenue des Etats Unis, Versailles Cedex, 78035, France

    B. Chauvin & A. Rouault

Authors
  1. B. Chauvin
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  2. A. Rouault
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Editor information

Editors and Affiliations

  1. Department of Mathematics and Statistics, Iowa State University, Ames, IA, 50011, USA

    Krishna B. Athreya

  2. School of Mathematics and Computing Science, Chalmers University of Technology, Gothenburg University, Gothenburg, S-412 96, Sweden

    Peter Jagers

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Chauvin, B., Rouault, A. (1997). Boltzmann-Gibbs Weights in the Branching Random Walk. In: Athreya, K.B., Jagers, P. (eds) Classical and Modern Branching Processes. The IMA Volumes in Mathematics and its Applications, vol 84. Springer, New York, NY. https://doi.org/10.1007/978-1-4612-1862-3_3

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  • DOI: https://doi.org/10.1007/978-1-4612-1862-3_3

  • Publisher Name: Springer, New York, NY

  • Print ISBN: 978-1-4612-7315-8

  • Online ISBN: 978-1-4612-1862-3

  • eBook Packages: Springer Book Archive

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