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