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A generalized Pólya urn and limit laws for the number of outputs in a family of random circuits

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  • José Moler
  • Fernando Plo
  • Henar Urmeneta

Abstract

We introduce a generalized Pólya urn model with the feature that the evolution of the urn is governed by a function which may change depending on the stage of the process, and we obtain a Strong Law of Large Numbers and a Central Limit Theorem for this model, using stochastic recurrence techniques. This model is used to represent the evolution of a family of acyclic directed graphs, called random circuits, which can be seen as logic circuits. The model provides asymptotic results for the number of outputs, that is, terminal nodes, of this family of random circuits. Copyright Sociedad de Estadística e Investigación Operativa 2013

Suggested Citation

  • José Moler & Fernando Plo & Henar Urmeneta, 2013. "A generalized Pólya urn and limit laws for the number of outputs in a family of random circuits," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 22(1), pages 46-61, March.
    • Handle: RePEc:spr:testjl:v:22:y:2013:i:1:p:46-61
    DOI: 10.1007/s11749-012-0292-4
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    References listed on IDEAS

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    1. Janson, Svante, 2004. "Functional limit theorems for multitype branching processes and generalized Pólya urns," Stochastic Processes and their Applications, Elsevier, vol. 110(2), pages 177-245, April.
    2. Pemantle, Robin & Skyrms, Brian, 2004. "Time to absorption in discounted reinforcement models," Stochastic Processes and their Applications, Elsevier, vol. 109(1), pages 1-12, January.
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    Cited by:

    1. Scott R. Konzem & Hosam M. Mahmoud, 2016. "Characterization and Enumeration of Certain Classes of Tenable Pólya Urns Grown by Drawing Multisets of Balls," Methodology and Computing in Applied Probability, Springer, vol. 18(2), pages 359-375, June.
    2. Panpan Zhang & Hosam M. Mahmoud, 2020. "On Nodes of Small Degrees and Degree Profile in Preferential Dynamic Attachment Circuits," Methodology and Computing in Applied Probability, Springer, vol. 22(2), pages 625-645, June.

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