Hostname: page-component-78c5997874-xbtfd Total loading time: 0 Render date: 2024-11-17T16:52:09.642Z Has data issue: false hasContentIssue false
  • English
  • Français

Coupling any number of balls in the infinite-bin model

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

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]
Get access Rights & Permissions [Opens in a new window]

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 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

[1] Aldous, D. and Pitman, J. (1983). The asymptotic speed and shape of a particle system. In Probability, Statistics and Analysis (London Math. Soc. Lecture Notes Ser. 79), Cambridge University Press, pp. 1–23. Google Scholar
[2] Foss, S. and Konstantopoulos, T. (2003). Extended renovation theory and limit theorems for stochastic ordered graphs. Markov Process. Relat. Fields 9, 413–468. Google Scholar
[3] Foss, S. and Zachary, S. (2013). Stochastic sequences with a regenerative structure that may depend both on the future and on the past. Adv. Appl. Prob. 45, 1083–1110. Google Scholar
[4] Mallein, B. and Ramassamy, S. (2016). Barak–Erdős graphs and the infinite-bin model. Preprint. Available at https://arxiv.org/abs/1610.04043. Google Scholar
[5] Trahtman, A. N. (2011). Modifying the upper bound on the length of minimal synchronizing word. In Fundamentals of Computation Theory (Lecture Notes Comput. Sci. 6914), Springer, Heidelberg, pp. 173–180. Google Scholar