Two Speed TASEP with Step Initial Condition

TL;DR

This paper analyzes the two-speed TASEP with step initial condition, extending previous models to include different particle hopping rates and providing new transition probability formulas.

Contribution

It introduces a solution for the transition probabilities of two-speed TASEP with step initial condition, expanding the understanding of asymmetric exclusion processes.

Findings

Derived transition probability formulas for two-speed TASEP with step initial condition

Extended previous models to include particles with different hopping rates

Provided analytical tools for studying asymmetric exclusion processes with complex initial conditions

Abstract

In this paper, we consider zero range process with an initial condition which is equivalent to step initial condition in total asymmetric simple exclusion process (TASEP) as described in a paper by R\'akos, A. and Sch\"utz by using techniques developed by Borodin, Ferrari, and Sasamoto. The solution for the transition probability of total asymmetric simple exclusion process for particles with different hopping rates was first worked out by Sch\"utz and Rak\"os (2005) for the case when $p=1$ or $q=1$. The formula was later applied to analyze two speed TASEP (Borodin, Ferrari, and Sasamoto, 2009) with alternating initial condition. Here we will investigate the two speed TASEP case with step initial condition.