Large time asymptotics of growth models on space-like paths II: PNG and parallel TASEP
- Borodin, Alexei
- Ferrari, Patrik
- Sasamoto, Tomohiro
2010 Mathematics Subject Classification
- 82C22 60K35 15A52
- Simple exclusion process, space-like universality, KPZ class, Airy processes
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. We also obtain the corresponding results for the discrete time TASEP (totally asymmetric simple exclusion process) with parallel update.