Flat PNG universality conjecture for the Airy one process

Let $h(x,t)$ be the height function of the polynuclear growth (PNG) model on a one-dimensional substrate with flat initial conditions. Let ${\cal A}_{\rm 1}$ denote the Airy one process. Flat PNG universality conjecture. The properly rescaled height function of the PNG model with flat initial conditions converges, in the large time limit, to the process ${\cal A}_{\rm 1}$. The one-point distribution for flat PNG is known to converge to the GOE Tracy–Widom distribution, and this conjecture extends the corresponding TASEP result to the full space-time process; the scaling exponents are expected to agree, with the coefficients determined by matching the PNG droplet case.