Stabilization time of finite configurations with a second class particle in discrete TASEP

TL;DR

This paper analyzes how the presence of a second class particle affects the stabilization time in finite configurations of particles under discrete TASEP dynamics, providing insights into the dynamics of such systems.

Contribution

It characterizes the additional stabilization time caused by a second class particle in finite TASEP configurations with Bernoulli initial measures.

Findings

Quantifies the impact of a second class particle on stabilization time.

Provides a detailed description of the stabilization process in finite TASEP configurations.

Enhances understanding of second class particle dynamics in discrete-time TASEP.

Abstract

We consider finite configurations of particles and holes sampled according to Bernoulli product measure and with a second class particle added to a random position. The stabilization time is the number of steps needed to reach an ordered state under discrete time TASEP dynamics with parallel update. We describe the additional time of stabilization caused by the presence of the second class particle.