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Synchronization and fluctuation theorems for interacting Friedman urns

Part of: Limit theorems Special processes Probability theory on algebraic and topological structures

Published online by Cambridge University Press:  09 December 2016

Neeraja Sahasrabudhe
Neeraja Sahasrabudhe*
Affiliation:
Indian Institute of Technology Bombay
*
* Postal address:Indian Institute of Technology Bombay, Powai, Mumbai, 400076, Maharashtra, India. Email address: [email protected]
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Abstract

We consider a model of N interacting two-colour Friedman urns. The interaction model considered is such that the reinforcement of each urn depends on the fraction of balls of a particular colour in that urn as well as the overall fraction of balls of that colour in all the urns combined together. We show that the urns synchronize almost surely and that the fraction of balls of each colour converges to the deterministic limit of one-half, which matches with the limit known for a single Friedman urn. Furthermore, we use the notion of stable convergence to obtain limit theorems for fluctuations around the synchronization limit.

Keywords

Interacting urn modelFriedman urnPólya urnsynchronizationstable convergencereinforcementfluctuation theorem

MSC classification

Primary: 60K35: Interacting random processes; statistical mechanics type models; percolation theory
Secondary: 60F05: Central limit and other weak theorems 60B10: Convergence of probability measures 60F99: None of the above, but in this section
Type
Research Papers
Information
Journal of Applied Probability , Volume 53 , Issue 4 , December 2016 , pp. 1221 - 1239
Copyright
Copyright © Applied Probability Trust 2016 

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