Large time asymptotics of growth models on space-like paths I: PushASEP

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 (13)

• Determinantal Processes and Independence
• Discrete polynuclear growth and determinantal processes
• Fluctuation properties of the TASEP with periodic initial configuration
• Exact Solution of the Master Equation for the Asymmetric Exclusion Process
• Eynard-Mehta theorem, Schur process, and their pfaffian analogs
• Random matrices and determinantal processes
• Transition between Airy_1 and Airy_2 processes and TASEP fluctuations
• Exact solutions for KPZ-type growth processes, random matrices, and equilibrium shapes of crystals
• Large time asymptotics of growth models on space-like paths II: PNG and parallel TASEP
• A two--parametric family of asymmetric exclusion processes and its exact solution
• 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