Stochastic six-vertex model

2014/07/24 by Alexei Borodin, Ivan Corwin, Vadim Gorin · 1 citation
Mathematics · Physics and Astronomy · #cond-mat.stat-mech #math-ph #math.MP #math.PR

paper · pdf · doi:10.1215/00127094-3166843

published as Duke Math. J. 165, no. 3 (2016), 563-624 · 45 pages, 8 figures

arxiv created 2014/07/24 · arxiv updated 2016/03/16

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 an earlier prediction of Gwa and Spohn (1992) that this system belongs to the KPZ universality class.

Cited by

• Irreversible Markov Dynamics and Hydrodynamics for KPZ States in the Stochastic Six Vertex Model
• The asymmetric five vertex model on a rectangle