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

45 pages, 8 figures

References in corpus (6)

• Probability Distribution of the Free Energy of the Continuum Directed Random Polymer in 1+1 dimensions
• Asymptotics in ASEP with Step Initial Condition
• Spectral theory for interacting particle systems solvable by coordinate Bethe ansatz
• Macdonald processes, quantum integrable systems and the Kardar-Parisi-Zhang universality class
• Lectures on the integrability of the 6-vertex model
• The 6-vertex model with fixed boundary conditions

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