Semi-infinite TASEP with a Complex Boundary Mechanism

TL;DR

This paper studies a semi-infinite TASEP with a complex boundary mechanism, proving a strong law of large numbers for particle entry using a novel multi-type particle system representation.

Contribution

It introduces a new boundary mechanism for TASEP and establishes a strong law of large numbers through a multi-type particle system approach.

Findings

Proved a strong law of large numbers for particle entry.

Developed a new multi-type particle system representation.

Extended understanding of boundary effects in TASEP.

Abstract

We consider a totally asymmetric exclusion process on the positive half-line. When particles enter in the system according to a Poisson source, Liggett has computed all the limit distributions when the initial distribution has an asymptotic density. In this paper we consider systems for which particles enter at the boundary according to a complex mechanism depending on the current configuration in a finite neighborhood of the origin. For this kind of models, we prove a strong law of large numbers for the number of particles entered in the system at a given time. Our main tool is a new representation of the model as a multi-type particle system with infinitely many particle types.