Open Access
2015 Multivariate juggling probabilities
Arvind Ayyer, Jérémie Bouttier, Sylvie Corteel, François Nunzi
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Electron. J. Probab. 20: 1-29 (2015). DOI: 10.1214/EJP.v20-3495


We consider refined versions of Markov chains related to juggling introduced by Warrington. We further generalize the construction to juggling with arbitrary heights as well as infinitely many balls, which are expressed more succinctly in terms of Markov chains on integer partitions. In all cases, we give explicit product formulas for the stationary probabilities and closed-form expressions for the normalization factor. We also refine and generalize enriched Markov chains on set partitions. Lastly, we prove that in one case, the stationary distribution is attained in finite time.


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Arvind Ayyer. Jérémie Bouttier. Sylvie Corteel. François Nunzi. "Multivariate juggling probabilities." Electron. J. Probab. 20 1 - 29, 2015.


Accepted: 15 January 2015; Published: 2015
First available in Project Euclid: 4 June 2016

zbMATH: 1320.60024
MathSciNet: MR3311218
Digital Object Identifier: 10.1214/EJP.v20-3495

Primary: 60C05 , 60J10
Secondary: 05A17 , 05A18 , 82C23

Keywords: combinatorics , Juggling , Markov chain

Vol.20 • 2015
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