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Coupling any number of balls in the infinite-bin model

Published online by Cambridge University Press:  22 June 2017

Ksenia Chernysh*
Affiliation:
Heriot-Watt University
Sanjay Ramassamy*
Affiliation:
Brown University
*
* Postal address: School of Mathematical and Computer Sciences, Heriot-Watt University, Edinburgh EH14 4AS, UK.
** Current address: Unité de Mathématiques Pures et Appliquées, École normale supérieure de Lyon, 46 allée d'Italie, 69364 Lyon Cedex 07, France. Email address: ramassam@math.brown.edu

Abstract

The infinite-bin model, introduced by Foss and Konstantopoulos (2003), describes the Markovian evolution of configurations of balls placed inside bins, obeying certain transition rules. We prove that we can couple the behaviour of any finite number of balls, provided at least two different transition rules are allowed. This coupling makes it possible to define the regeneration events needed by Foss and Zachary (2013) to prove convergence results for the distribution of the balls.

Type
Research Papers
Copyright
Copyright © Applied Probability Trust 2017 

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References

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