Determinantal Expressions in Multi-Species TASEP

TL;DR

This paper studies multi-species TASEP models, revealing their multi-point height distributions have a determinantal structure and showing Gaussian fluctuations in certain cases, using couplings with coalescing random walks.

Contribution

It introduces a determinantal framework for multi-species TASEP height functions and connects their fluctuations to Gaussian limits in specific scenarios.

Findings

Multi-point distributions are determinantal.

Height fluctuations converge to Gaussian in homogeneous case.

Coupling with coalescing random walks underpins the analysis.

Abstract

Consider an inhomogeneous multi-species TASEP with drift to the left, and define a height function which equals the maximum species number to the left of a lattice site. For each fixed time, the multi-point distributions of these height functions have a determinantal structure. In the homogeneous case and for certain initial conditions, the fluctuations of the height function converge to Gaussian random variables in the large-time limit. The proof utilizes a coupling between the multi-species TASEP and a coalescing random walk, and previously known results for coalescing random walks.