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15 February 2016 Stochastic six-vertex model
Alexei Borodin, Ivan Corwin, Vadim Gorin
Duke Math. J. 165(3): 563-624 (15 February 2016). DOI: 10.1215/00127094-3166843

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.

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Alexei Borodin. Ivan Corwin. Vadim Gorin. "Stochastic six-vertex model." Duke Math. J. 165 (3) 563 - 624, 15 February 2016. https://doi.org/10.1215/00127094-3166843

Information

Received: 5 August 2014; Revised: 28 March 2015; Published: 15 February 2016
First available in Project Euclid: 20 November 2015

zbMATH: 1343.82013
MathSciNet: MR3466163
Digital Object Identifier: 10.1215/00127094-3166843

Subjects:
Primary: 82B20
Secondary: 60K35

Rights: Copyright © 2016 Duke University Press

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Vol.165 • No. 3 • 15 February 2016
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