Shock fluctuations in TASEP under a variety of time scalings

TL;DR

This paper analyzes shock fluctuations in TASEP with different initial conditions, deriving exact formulas for second class particle distributions and studying their limiting behaviors under various time scalings.

Contribution

It introduces a multicolored TASEP approach to obtain exact distribution formulas and explores how shock fluctuations depend on different time scaling regimes.

Findings

Exact formulas for second class particle distributions

Limiting distributions vary with time scaling

Shock fluctuation behavior depends on initial block scaling

Abstract

We consider the totally asymmetric simple exclusion process (TASEP) with two different initial conditions with shock discontinuities formed by blocks of fully packed particles. Initially a second class particle is at the left of a shock discontinuity. Using multicolored TASEP we derive exact formulas for the distribution of the second class particle and colored height functions. These are given in terms of the height function at different positions of a single TASEP configuration. We study the limiting distributions of second class particles (and colored height functions). The result depends on how the width blocks of particles scale with the observation time; we study a variety of such scalings.