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2 results

  • Random systems in ultrametric spaces

  • Part of
  • D. A. Dawson, L. G. Gorostiza
  • Journal:
    Advances in Applied Probability / Volume 50 / Issue A / December 2018
    Published online by Cambridge University Press:
    01 February 2019, pp. 83-97
    Print publication:
    December 2018
    • Article
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  • We discuss percolation and random walks in a class of homogeneous ultrametric spaces together with similarities and differences in ultrametric and Euclidean spaces. We briefly outline the role of these models in the study of interacting systems. Several open problems are presented.

  • Synchronization via Interacting Reinforcement

  • Part of
  • Paolo Dai Pra, Pierre-Yves Louis, Ida G. Minelli
  • Journal:
    Journal of Applied Probability / Volume 51 / Issue 2 / June 2014
    Published online by Cambridge University Press:
    19 February 2016, pp. 556-568
    Print publication:
    June 2014
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  • We consider a system of urns of Pólya type, containing balls of two colors; the reinforcement of each urn depends on both the content of the urn and the average content of all urns. We show that the urns synchronize almost surely, in the sense that the fraction of balls of a given color converges almost surely as time tends to ∞ to the same limit for all urns. A normal approximation for a large number of urns is also obtained.