Statistics of TASEP with three merging characteristics

TL;DR

This paper analyzes the particle fluctuation behavior at the merging point of three shock waves in TASEP with piecewise constant initial densities, revealing a distribution described by a product of three GOE Tracy-Widom functions.

Contribution

It provides a direct TASEP analysis of the merging shock fluctuations, demonstrating a novel distribution involving a product of three Tracy-Widom GOE functions.

Findings

Particle fluctuations at the merging point follow a product of three GOE Tracy-Widom distributions.

The study works directly within TASEP without using last passage percolation techniques.

Results extend understanding of shock merging phenomena in exclusion processes.

Abstract

In this paper we consider the totally asymmetric simple exclusion process, with non-random initial condition having three regions of constant densities of particles. From left to right, the densities of the three regions are increasing. Consequently, there are three characteristics which meet, i.e. two shocks merge. We study the particle fluctuations at this merging point and show that they are given by a product of three (properly scaled) GOE Tracy-Widom distribution functions. We work directly in TASEP without relying on the connection to last passage percolation.