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August 2019 Limit law of a second class particle in TASEP with non-random initial condition
P. L. Ferrari, P. Ghosal, P. Nejjar
Ann. Inst. H. Poincaré Probab. Statist. 55(3): 1203-1225 (August 2019). DOI: 10.1214/18-AIHP916

Abstract

We consider the totally asymmetric simple exclusion process (TASEP) with non-random initial condition and density $\lambda$ on $\mathbb{Z}_{-}$ and $\rho$ on $\mathbb{Z}_{+}$, and a second class particle initially at the origin. For $\lambda<\rho$, there is a shock and the second class particle moves with speed $1-\lambda-\rho$. For large time $t$, we show that the position of the second class particle fluctuates on the $t^{1/3}$ scale and determine its limiting law. We also obtain the limiting distribution of the number of steps made by the second class particle until time $t$.

On considère le processus d’exclusion simple totalement asymétrique avec des condition initiales déterministes, densité $\lambda$ sur $\mathbb{Z}_{-}$ et $\rho$ sur $\mathbb{Z}_{+}$. Initialement on place une particule de deuxième classe à l’origine. Si $\lambda<\rho$, un choc est créé et la particule de deuxième classe le suit avec vitesse $1-\lambda-\rho$. Dans la limite $t\to\infty$, on démontre que les fluctuations de la position de la particule de deuxième classe sont de l’ordre $t^{1/3}$ et on obtient sa loi limite. On détermine aussi la loi limite du nombre de sauts faits par la particule de deuxième classe jusqu’à l’instant $t$.

Citation

Download Citation

P. L. Ferrari. P. Ghosal. P. Nejjar. "Limit law of a second class particle in TASEP with non-random initial condition." Ann. Inst. H. Poincaré Probab. Statist. 55 (3) 1203 - 1225, August 2019. https://doi.org/10.1214/18-AIHP916

Information

Received: 26 October 2017; Revised: 4 May 2018; Accepted: 21 May 2018; Published: August 2019
First available in Project Euclid: 25 September 2019

zbMATH: 07133719
MathSciNet: MR4010933
Digital Object Identifier: 10.1214/18-AIHP916

Subjects:
Primary: 60B20, 60K35, 82C22

Rights: Copyright © 2019 Institut Henri Poincaré

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Vol.55 • No. 3 • August 2019
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