Annales de l'Institut Henri Poincaré, Probabilités et Statistiques

Height fluctuations of stationary TASEP on a ring in relaxation time scale

Zhipeng Liu

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Abstract

We consider the totally asymmetric simple exclusion process on a ring with stationary initial conditions. The crossover between KPZ dynamics and equilibrium dynamics occurs when time is proportional to the $3/2$ power of the ring size. We obtain the limit of the height function along the direction of the characteristic line in this time scale. The two-point covariance function in this scale is also discussed.

Résumé

Nous considérons le processus d’exclusion simple totalement asymétrique sur un anneau, avec condition initiale stationnaire. La transition entre la dynamique KPZ et la dynamique d’équilibre a lieu lorsque le temps est proportionnel à la puissance $3/2$ de la taille de l’anneau. Nous obtenons la limite de la fonction de hauteur le long de la droite caractéristique dans cette échelle de temps. Nous étudions également la fonction de covariance à deux points dans cette même échelle.

Article information

Source
Ann. Inst. H. Poincaré Probab. Statist., Volume 54, Number 2 (2018), 1031-1057.

Dates
Received: 14 October 2016
Revised: 1 March 2017
Accepted: 17 March 2017
First available in Project Euclid: 25 April 2018

Permanent link to this document
https://projecteuclid.org/euclid.aihp/1524643239

Digital Object Identifier
doi:10.1214/17-AIHP831

Mathematical Reviews number (MathSciNet)
MR3795076

Zentralblatt MATH identifier
06866679

Subjects
Primary: 60K35: Interacting random processes; statistical mechanics type models; percolation theory [See also 82B43, 82C43]

Keywords
TASEP on a ring Stationary initial condition Relaxation time scale

Citation

Liu, Zhipeng. Height fluctuations of stationary TASEP on a ring in relaxation time scale. Ann. Inst. H. Poincaré Probab. Statist. 54 (2018), no. 2, 1031--1057. doi:10.1214/17-AIHP831. https://projecteuclid.org/euclid.aihp/1524643239


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