Electronic Journal of Probability
- Electron. J. Probab.
- Volume 20 (2015), paper no. 5, 29 pp.
Multivariate juggling probabilities
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.
Electron. J. Probab., Volume 20 (2015), paper no. 5, 29 pp.
Accepted: 15 January 2015
First available in Project Euclid: 4 June 2016
Permanent link to this document
Digital Object Identifier
Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
Primary: 60C05: Combinatorial probability 60J10: Markov chains (discrete-time Markov processes on discrete state spaces)
Secondary: 05A17: Partitions of integers [See also 11P81, 11P82, 11P83] 05A18: Partitions of sets 82C23: Exactly solvable dynamic models [See also 37K60]
This work is licensed under aCreative Commons Attribution 3.0 License.
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