## Electronic Journal of Probability

### Multivariate juggling probabilities

#### Abstract

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.

#### Article information

Source
Electron. J. Probab., Volume 20 (2015), paper no. 5, 29 pp.

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

https://projecteuclid.org/euclid.ejp/1465067111

Digital Object Identifier
doi:10.1214/EJP.v20-3495

Mathematical Reviews number (MathSciNet)
MR3311218

Zentralblatt MATH identifier
1320.60024

Rights

#### Citation

Ayyer, Arvind; Bouttier, Jérémie; Corteel, Sylvie; Nunzi, François. Multivariate juggling probabilities. Electron. J. Probab. 20 (2015), paper no. 5, 29 pp. doi:10.1214/EJP.v20-3495. https://projecteuclid.org/euclid.ejp/1465067111

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