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Coupling any number of balls in the infinite-bin model

Part of: Markov processes Discrete mathematics in relation to computer science

Published online by Cambridge University Press:  22 June 2017

Ksenia Chernysh  and
Sanjay Ramassamy
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: [email protected]
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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.

Keywords

Markov chaincouplinginfinite-bin model

MSC classification

Primary: 60J10: Markov chains (discrete-time Markov processes on discrete state spaces)
Secondary: 68R05: Combinatorics
Type
Research Papers
Information
Journal of Applied Probability , Volume 54 , Issue 2 , June 2017 , pp. 540 - 549
Copyright
Copyright © Applied Probability Trust 2017 

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References

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