Stochastic six-vertex model

By Alexei Borodin, Ivan Corwin, Vadim Gorin. 2014

161 citations recorded by the source corpus.

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.

View Paper: https://www.semanticscholar.org/paper/4cbdcd7bac16e2d0030e06dc0e98cd8be56ecc52

Citations in the corpus

• On a family of symmetric rational functions (2014, methodology): “In a very recent work of Borodin-Corwin-Gorin [4], these functions were also utilized for asymptotic analysis of stochastic (spin 1 2 ) six vertex model in a quadrant.”