Electronic Journal of Probability

Multivariate juggling probabilities

Arvind Ayyer, Jérémie Bouttier, Sylvie Corteel, and François Nunzi

Full-text: Open access

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

Permanent link to this document
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

Subjects
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]

Keywords
Markov chain Combinatorics Juggling

Rights
This work is licensed under aCreative Commons Attribution 3.0 License.

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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