Duke Mathematical Journal

Stochastic six-vertex model

Alexei Borodin, Ivan Corwin, and Vadim Gorin

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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

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

Received: 5 August 2014
Revised: 28 March 2015
First available in Project Euclid: 20 November 2015

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 82B20: Lattice systems (Ising, dimer, Potts, etc.) and systems on graphs
Secondary: 60K35: Interacting random processes; statistical mechanics type models; percolation theory [See also 82B43, 82C43]

Six-vertex model height function interacting particle system KPZ universality


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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