## Duke Mathematical Journal

### Stochastic six-vertex model

#### Abstract

We study the asymmetric six-vertex model in the quadrant with parameters on the stochastic line. We show that the random height function of the model converges to an explicit deterministic limit shape as the mesh size tends to $0$. We further prove that the one-point fluctuations around the limit shape are asymptotically governed by the GUE Tracy–Widom distribution. We also explain an equivalent formulation of our model as an interacting particle system, which can be viewed as a discrete time generalization of ASEP started from the step initial condition. Our results confirm a 1992 prediction of Gwa and Spohn that this system belongs to the KPZ universality class.

#### Article information

Source
Duke Math. J., Volume 165, Number 3 (2016), 563-624.

Dates
Revised: 28 March 2015
First available in Project Euclid: 20 November 2015

https://projecteuclid.org/euclid.dmj/1448028098

Digital Object Identifier
doi:10.1215/00127094-3166843

Mathematical Reviews number (MathSciNet)
MR3466163

Zentralblatt MATH identifier
1343.82013

#### Citation

Borodin, Alexei; Corwin, Ivan; Gorin, Vadim. Stochastic six-vertex model. Duke Math. J. 165 (2016), no. 3, 563--624. doi:10.1215/00127094-3166843. https://projecteuclid.org/euclid.dmj/1448028098

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