Limits of multilevel TASEP and similar processes
Annales de l'I.H.P. Probabilités et statistiques, Tome 51 (2015) no. 1, pp. 18-27.

Nous étudions le comportement asymptotique d’une classe de dynamiques aléatoires sur des configurations entrelacées de particules (dites aussi motifs de Gelfand–Tsetlin). Des exemples de telles dynamiques incluent, en particulier, une extension à plusieurs niveaux du TASEP et des dynamiques de particules reliées à l’algorithme de mélange pour les pavages par dominos du diamant aztèque. Nous montrons que le processus des mouvements browniens réfléchis entrelacés introduit par Warren dans (Electron. J. Probab. 12 (2007) 573–590) est une limite d’échelle universelle pour ces dynamiques.

We study the asymptotic behavior of a class of stochastic dynamics on interlacing particle configurations (also known as Gelfand–Tsetlin patterns). Examples of such dynamics include, in particular, a multi-layer extension of TASEP and particle dynamics related to the shuffling algorithm for domino tilings of the Aztec diamond. We prove that the process of reflected interlacing Brownian motions introduced by Warren in (Electron. J. Probab. 12 (2007) 573–590) serves as a universal scaling limit for such dynamics.

DOI : 10.1214/13-AIHP555
Classification : 60J27, 60K35, 60F17
Mots-clés : interacting particle system, exclusion process, reflected brownian motion 
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Gorin, Vadim; Shkolnikov, Mykhaylo. Limits of multilevel TASEP and similar processes. Annales de l'I.H.P. Probabilités et statistiques, Tome 51 (2015) no. 1, pp. 18-27. doi : 10.1214/13-AIHP555. http://www.numdam.org/articles/10.1214/13-AIHP555/

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