Large time asymptotics of growth models on space-like paths II: PNG and parallel TASEP

Understand

We consider the polynuclear growth (PNG) model in 1+1 dimension with flat initial condition and no extra constraints.

• The joint distributions of surface height at finitely many points at a fixed time moment are given as marginals of a signed determinantal point process.
• The long time scaling limit of the surface height is shown to coincide with the Airy_1 process.
• This result holds more generally for the observation points located along any space-like path in the space-time plane.