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

• José Moler ^[1] ; Fernando Plo ^[2] ; Henar Urmeneta ^[1]
  1. [1] Universidad Pública de Navarra

     Universidad Pública de Navarra

     Pamplona, España

     
  2. [2] Universidad de Zaragoza

     Universidad de Zaragoza

     Zaragoza, España

     
• Localización: Test: An Official Journal of the Spanish Society of Statistics and Operations Research, ISSN-e 1863-8260, ISSN 1133-0686, Vol. 22, Nº. 1, 2013, págs. 46-61
• Idioma: inglés
• DOI: 10.1007/s11749-012-0292-4
• Texto completo no disponible (Saber más ...)
• Resumen

  • 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