Stochastic six-vertex model

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