Annales de l'Institut Henri Poincaré, Probabilités et Statistiques

Limits of multilevel TASEP and similar processes

Vadim Gorin and Mykhaylo Shkolnikov

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Abstract

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.

Résumé

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.

Article information

Source
Ann. Inst. H. Poincaré Probab. Statist., Volume 51, Number 1 (2015), 18-27.

Dates
First available in Project Euclid: 14 January 2015

Permanent link to this document
https://projecteuclid.org/euclid.aihp/1421244397

Digital Object Identifier
doi:10.1214/13-AIHP555

Mathematical Reviews number (MathSciNet)
MR3300962

Zentralblatt MATH identifier
1312.60116

Subjects
Primary: 60J27: Continuous-time Markov processes on discrete state spaces 60K35: Interacting random processes; statistical mechanics type models; percolation theory [See also 82B43, 82C43] 60F17: Functional limit theorems; invariance principles

Keywords
Interacting particle system Exclusion process Reflected Brownian motion

Citation

Gorin, Vadim; Shkolnikov, Mykhaylo. Limits of multilevel TASEP and similar processes. Ann. Inst. H. Poincaré Probab. Statist. 51 (2015), no. 1, 18--27. doi:10.1214/13-AIHP555. https://projecteuclid.org/euclid.aihp/1421244397


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