Large time asymptotics of growth models on space-like paths I: PushASEP
arXiv:0707.2813
Abstract
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 Airy_1 and 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.
48 pages, 4 figures, LaTeX; Final version
References in corpus (4)
- Transition between Airy_1 and Airy_2 processes and TASEP fluctuations
- Determinantal transition kernels for some interacting particles on the line
- Bethe ansatz and current distribution for the TASEP with particle-dependent hopping rates
- The universal Airy_1 and Airy_2 processes in the Totally Asymmetric Simple Exclusion Process