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Multivariate juggling probabilities. (English) Zbl 1331.60021
Bousquet-Mélou, Mireille (ed.) et al., Proceeding of the 25th international conference on probabilistic, combinatorial and asymptotic methods in the analysis of algorithms, AofA’14, UPMC-Jussieu, Paris, France, June 16–20, 2014. Nancy: The Association. Discrete Mathematics & Theoretical Computer Science (DMTCS). Discrete Mathematics and Theoretical Computer Science (DMTCS-HAL). Proceedings BA, 1-12 (2014).
Summary: We consider refined versions of Markov chains related to juggling. 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.
For the entire collection see [Zbl 1329.68022].

MSC:
60C05 Combinatorial probability
60J10 Markov chains (discrete-time Markov processes on discrete state spaces)
05A17 Combinatorial aspects of partitions of integers
05A18 Partitions of sets
82C23 Exactly solvable dynamic models in time-dependent statistical mechanics
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