The second class particle in the half-line open TASEP

TL;DR

This paper analyzes the behavior of the second class particle in half-line open TASEP under shock conditions, deriving exact distribution formulas and studying their asymptotic behavior under different scalings.

Contribution

It introduces exact distribution formulas for the second class particle in half-line open TASEP using color-position symmetry and explores their asymptotic distributions.

Findings

Derived exact formulas for the second class particle distribution.

Analyzed asymptotic behavior under constant and KPZ-type scalings.

Provided insights into shock discontinuities in half-line open TASEP.

Abstract

We consider the second class particle in half-line open TASEP under two different initial conditions with shock discontinuities. The exact formulas for the distribution of the second class particle can be derived by using the color-position symmetry theorem of colored half-space TASEP. We study the asymptotic distribution of second class particles under the constant scaling and KPZ-type scaling.