Publication : t14/044

Multivariate Juggling Probabilities

Ayyer A. (Department of Mathematics, Indian Institute of Science, Bangalore, 560 012, India)
Bouttier J. (CEA, IPhT (Institut de Physique Théorique), F-91191 Gif-sur-Yvette, France)
Corteel S. (LIAFA, CNRS et Université Paris Diderot, Case 7014, F-75205 Paris Cedex 13)
Nunzi F. (CEA, IPhT (Institut de Physique Théorique), F-91191 Gif-sur-Yvette, France)
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.
Année de publication : 2015
Revue : Electronic Journal of Probability 20 1-29 (2015)
DOI : 10.1214/EJP.v20-3495
Preprint : arXiv:1402.3752
Lien :
Keywords : Markov chain, Combinatorics, Juggling
Langue : Anglais

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