Leaders in multi-type TASEP

TL;DR

This paper investigates the behavior of the leader particle in a multi-type TASEP on the integer lattice, establishing a CLT and connecting the problem to voter and coalescing processes, with analysis of related observables.

Contribution

It introduces a central limit theorem for the leader's position in multi-type TASEP and links it to voter and coalescing process observables, providing new asymptotic results.

Findings

CLT for the leader particle position in multi-type TASEP

Asymptotic behavior of voter and coalescing process observables

Analysis of multi-particle observables at large times

Abstract

We study the totally asymmetric simple exclusion process (TASEP) on $\mathbb{Z}$ with step initial condition, in which all particles have distinct types. Our main object of interest is the type of the rightmost particle -- the leader -- at large time $t$. We prove a central limit theorem for this random variable. Somewhat unexpectedly, the problem is closely connected to certain observables of voter and coalescing processes on $\mathbb{Z}$; we therefore derive their asymptotics as well. We also analyze the large-time behavior of a few other related observables, including certain multi-particle ones.