Hall-Littlewood-PushTASEP and its KPZ limit

Abstract

We study a new model of interactive particle systems which we call the randomly activated cascading exclusion process (RACEP). Particles wake up according to exponential clocks and then take a geometric number of steps. If another particle is encountered during these steps, the first particle goes to sleep at that location and the second is activated and proceeds accordingly. We consider a totally asymmetric version of this model which we refer as Hall-Littlewood-PushTASEP (HL-PushTASEP) on ${\mathbb{Z}}_{\ge 0}$ lattice where particles only move right and where initially particles are distributed according to Bernoulli product measure on ${\mathbb{Z}}_{\ge 0}$. We prove KPZ-class limit theorems for the height function fluctuations. Under a particular weak scaling, we also prove convergence to the solution of the KPZ equation.

71 Pages, 6 figures

References in corpus (5)

• Probability Distribution of the Free Energy of the Continuum Directed Random Polymer in 1+1 dimensions
• Asymptotics in ASEP with Step Initial Condition
• The one-dimensional KPZ equation and its universality class
• A Fredholm Determinant Representation in ASEP
• A phase transition for $q$-TASEP with a few slower particles

Cited by in corpus (2)

• Some recent progress in singular stochastic PDEs
• Stationary Higher Spin Six Vertex Model and $q$-Whittaker measure