Generalized Interacting Urn Models

Abstract

Interacting urns with exponential reinforcement were introduced and studied in Launay (2011). As its parameter $\rho$ tends to $\iy$, this reinforcement mechanism converges to the "generalized" reinforcement, in which the probability of draw may be 0 or 1 for some of the colors, depending on the current configuration. For a single urn, the generalized reinforcement is easy to analyse. We introduce and study the generalized interacting urn model with two or more urns and two colors. Our results concern the law of the so-called non-conformist urns, and answer in the asymptotic sense one of the open questions from the above mentioned paper.

16 pages, 7 figures

References in corpus (1)

• A survey of random processes with reinforcement

Cited by in corpus (5)

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• Interacting generalized Friedman's urn systems
• Synchronization of Reinforced Stochastic Processes with a Network-based Interaction
• Pólya Urn Schemes with Infinitely Many Colors
• Networks of reinforced stochastic processes: a complete description of the first-order asymptotics