December 2016 Synchronization and fluctuation theorems for interacting Friedman urns
Neeraja Sahasrabudhe
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J. Appl. Probab. 53(4): 1221-1239 (December 2016).

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.

Citation

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Neeraja Sahasrabudhe. "Synchronization and fluctuation theorems for interacting Friedman urns." J. Appl. Probab. 53 (4) 1221 - 1239, December 2016.

Information

Published: December 2016
First available in Project Euclid: 7 December 2016

zbMATH: 1356.60173
MathSciNet: MR3581253

Subjects:
Primary: 60K35
Secondary: 60B10 , 60F05 , 60F99

Keywords: Fluctuation theorem , Friedman urn , Interacting urn model , Pólya urn , Reinforcement , stable convergence , synchronization

Rights: Copyright © 2016 Applied Probability Trust

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Vol.53 • No. 4 • December 2016
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