## Large time asymptotics of growth models on space-like paths. I: Push ASEP.(English)Zbl 1187.82084

Summary: We consider a new interacting particle system on the one-dimensional lattice that interpolates between TASEP and Toom’s model: A particle cannot jump to the right if the neighboring site is occupied, and when jumping to the left it simply pushes all the neighbors that block its way. We prove that for flat and step initial conditions, the large time fluctuations of the height function of the associated growth model along any space-like path are described by the $$\text{Airy}_1$$ and $$\text{Airy}_2$$ processes. This includes fluctuations of the height profile for a fixed time and fluctuations of a tagged particle’s trajectory as special cases.

### MSC:

 82C22 Interacting particle systems in time-dependent statistical mechanics 60K35 Interacting random processes; statistical mechanics type models; percolation theory 15B52 Random matrices (algebraic aspects)

### Keywords:

stochastic growth; KPZ; determinantal processes; Airy processes
Full Text: