Translator Disclaimer
2015 Tracy-Widom limit of $q$-Hahn TASEP
Bálint Vető
Author Affiliations +
Electron. J. Probab. 20: 1-22 (2015). DOI: 10.1214/EJP.v20-4241

Abstract

We consider the $q$-Hahn TASEP which is a three-parameter family of discrete time interacting particle systems. The particles jump to the right independently according to a certain $q$-Binomial distribution with parallel updates. It is a generalization of the totally asymmetric simple exclusion process (TASEP) on $\mathbb{Z}$. For step initial condition, we prove that the current fluctuation of $q$-Hahn TASEP at time $\tau$ is of order $\tau^{1/3}$ and asymptotically distributed as the GUE Tracy–Widom distribution. We verify the KPZ scaling theory conjecture for the $q$-Hahn TASEP.

Citation

Download Citation

Bálint Vető. "Tracy-Widom limit of $q$-Hahn TASEP." Electron. J. Probab. 20 1 - 22, 2015. https://doi.org/10.1214/EJP.v20-4241

Information

Accepted: 29 September 2015; Published: 2015
First available in Project Euclid: 4 June 2016

zbMATH: 1328.60221
MathSciNet: MR3407219
Digital Object Identifier: 10.1214/EJP.v20-4241

Subjects:
Primary: 60K35
Secondary: 60B20

JOURNAL ARTICLE
22 PAGES


SHARE
Vol.20 • 2015
Back to Top