Stochastic six-vertex model in a half-quadrant and half-line open ASEP

Understand

We consider the asymmetric simple exclusion process (ASEP) on the positive integers with an open boundary condition.

• We show that, when starting devoid of particles and for a certain boundary condition, the height function at the origin fluctuates asymptotically (in large time $\tau$) according to the Tracy-Widom GOE distribution on the $\tau^{1/3}$ scale.
• This is the first example of KPZ asymptotics for a half-space system outside the class of free-fermionic/determinantal/Pfaffian models.
• Our main tool in this analysis is a new class of probability measures on Young diagrams that we call half-space Macdonald processes, as well as two surprising relations.