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Multivariate juggling probabilities

Ayyer, Arvind and Bouttier, Jeremie and Corteel, Sylvie and Nunzi, Francois (2015) Multivariate juggling probabilities. In: ELECTRONIC JOURNAL OF PROBABILITY, 20 .

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Official URL: http://dx.doi.org/10.1214/EJP.v20-3495

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. The normalization factor in one case can be explicitly written as a homogeneous symmetric polynomial. We also refine and generalize enriched Markov chains on set partitions. Lastly, we prove that in one case, the stationary distribution is attained in bounded time.

Item Type: Journal Article
Additional Information: Copy right for this article belongs to the UNIV WASHINGTON, DEPT MATHEMATICS, BOX 354350, SEATTLE, WASHINGTON 98195-4350 USA
Keywords: Markov chain; Combinatorics; Juggling
Department/Centre: Division of Physical & Mathematical Sciences > Mathematics
Depositing User: Id for Latest eprints
Date Deposited: 20 Apr 2015 07:34
Last Modified: 20 Apr 2015 07:34
URI: http://eprints.iisc.ac.in/id/eprint/51257

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