Electronic Journal of Probability

Tracy-Widom limit of $q$-Hahn TASEP

Bálint Vető

Full-text: Open access

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.

Article information

Source
Electron. J. Probab., Volume 20 (2015), paper no. 102, 22 pp.

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

Permanent link to this document
https://projecteuclid.org/euclid.ejp/1465067208

Digital Object Identifier
doi:10.1214/EJP.v20-4241

Mathematical Reviews number (MathSciNet)
MR3407219

Zentralblatt MATH identifier
1328.60221

Subjects
Primary: 60K35: Interacting random processes; statistical mechanics type models; percolation theory [See also 82B43, 82C43]
Secondary: 60B20: Random matrices (probabilistic aspects; for algebraic aspects see 15B52)

Keywords
interacting particle systems KPZ universality class q-Hahn TASEP current fluctuation Tracy–Widom distribution

Rights
This work is licensed under aCreative Commons Attribution 3.0 License.

Citation

Vető, Bálint. Tracy-Widom limit of $q$-Hahn TASEP. Electron. J. Probab. 20 (2015), paper no. 102, 22 pp. doi:10.1214/EJP.v20-4241. https://projecteuclid.org/euclid.ejp/1465067208


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