Bumping sequences and multispecies juggling - CNRS - Centre national de la recherche scientifique Accéder directement au contenu
Article Dans Une Revue Advances in Applied Mathematics Année : 2018

Bumping sequences and multispecies juggling

Résumé

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.
Fichier principal
Vignette du fichier
multispecies_arxiv3.pdf (553.69 Ko) Télécharger le fichier
Origine : Fichiers produits par l'(les) auteur(s)
Loading...

Dates et versions

hal-01141430 , version 1 (29-03-2018)

Identifiants

Citer

Arvind Ayyer, Jérémie Bouttier, Sylvie Corteel, Svante Linusson, François Nunzi. Bumping sequences and multispecies juggling. Advances in Applied Mathematics, 2018, 98, pp.100-126. ⟨10.1016/j.aam.2018.03.001⟩. ⟨hal-01141430⟩
557 Consultations
87 Téléchargements

Altmetric

Partager

Gmail Facebook X LinkedIn More