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Bumping sequences and multispecies juggling

Ayyer, Arvind and Bouttier, Jeremie and Corteel, Sylvie and Linusson, Svante and Nunzi, Francois (2018) Bumping sequences and multispecies juggling. In: ADVANCES IN APPLIED MATHEMATICS, 98 . pp. 100-126.

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Official URL: http://dx.doi.org/10.1016/j.aam.2018.03.001

Abstract

Building on previous work by four of us (ABCN), we consider further generalizations of Warrington's juggling Markov chains. We first introduce ``multispecies'' juggling, which consist in having balls of different weights: when a ball is thrown it can possibly bump into a lighter ball that is then sent to a higher position, where it can in turn bump an even lighter ball, etc. We both study the case where the number of balls of each species is conserved and the case where the juggler sends back a ball of the species of its choice. In this latter case, we actually discuss three models: add-drop, annihilation and overwriting. The first two are generalisations of models presented in (ABCN) while the third one is new and its Markov chain has the ultra fast convergence property. We finally consider the case of several jugglers exchanging balls. In all models, we give explicit product formulas for the stationary probability and closed form expressions for the normalisation factor if known. (C) 2018 Elsevier Inc. All rights reserved.

Item Type: Journal Article
Additional Information: Copy right for this article belong to ACADEMIC PRESS INC ELSEVIER SCIENCE, 525 B ST, STE 1900, SAN DIEGO, CA 92101-4495 USA
Department/Centre: Division of Physical & Mathematical Sciences > Mathematics
Depositing User: Id for Latest eprints
Date Deposited: 05 Jun 2018 14:08
Last Modified: 05 Jun 2018 14:08
URI: http://eprints.iisc.ac.in/id/eprint/59935

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