Asymptotics in Random Recursive Circuits*

Abstract

A random recursive circuit is a combinatorial structure with a stochastic growth rule. These models are profusely used in computer science as data structures and in other fields, such as biostatistics, to model the spread of epidemics. The evolution of this random structure can be described by means of a generalized Polya urn model where different colors of balls represent different kind of nodes of the circuit. We prove that the process that represents the proportion of balls of each color fits a Robbins–Monro stochastic recurrence scheme and, then, sufficient conditions are established in order to obtain almost sure convergence and a central limit theorem for this process.