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

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