Abstract:

We study the model of the totally asymmetric exclusion process with generalized update (GTASEP), which compared to the usual totally asymmetric exclusion process, has an additional parameter enhancing clustering of particles. When the parameter varies in its range, the model transforms from the totally asymmetric exclusion process in discrete time with parallel update to what we call the deterministic aggregation (DA). We proved the integrability of the model and studied its behavior on a ring and on an infinite lattice.

In the case of ring geometry, we study the stationary state correlations, the cluster size distribution and the large-time fluctuations of integrated particle current. We derive the large deviation function for particle current, which interpolates between Derrida-Lebowitz universal function for Kardar–Parisi–Zhang (KPZ) class and a function for single particle diffusion when a ratio of the interaction parameter and the system size changes.

We study functional forms of distributions of particles position on an infinite lattice in the scaling limit for two types of initial conditions: step and alternating. For the moderate value of the attraction parameter, well-known Airy processes are obtained. In the case of large value of the attraction parameter we describe the transition between KPZ scaling behavior and the case where the KPZ universality breaks down.

(Based on candidate’s dissertation)