Two-Point Convergence of the Stochastic Six-Vertex Model to the Airy Process

In this paper we consider the stochastic six-vertex model in quadrant started with step initial data. After a long time T, it is known that one-point height function fluctuations are of order $$T^{1/3}$$ and governed by Tracy–Widom distribution. We prove two-point distribution function, rescaled horizontally $$T^{2/3}$$ vertically , converges to Airy process. The starting point result recent connection discovered Borodin–Bufetov–Wheeler between ascending Hall–Littlewood process (a certain measure on plane partitions). Using Macdonald difference operators, obtain formulas for observables process, which give access joint cumulative its function. A careful asymptotic analysis these gives convergence under restrictions parameters model.