Multivariate Juggling Probabilities

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.
Complete list of metadatas

https://hal-cea.archives-ouvertes.fr/cea-00979566
Contributor : Jérémie Bouttier <>
Submitted on : Wednesday, April 16, 2014 - 12:07:02 PM
Last modification on : Wednesday, August 7, 2019 - 12:19:20 PM

Links full text

Identifiers

Relations

Citation

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

Share

Metrics

Record views

435