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Journal Articles Electronic Journal of Probability Year : 2015

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. 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.

Dates and versions

cea-00979566 , version 1 (16-04-2014)



Arvind Ayyer, Jérémie Bouttier, Sylvie Corteel, François Nunzi. Multivariate Juggling Probabilities. Electronic Journal of Probability, 2015, 20 (5), pp.1-29. ⟨10.1214/EJP.v20-3495⟩. ⟨cea-00979566⟩


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