Fluctuation properties of the TASEP with periodic initial configuration

TL;DR

This paper analyzes the fluctuation properties of the TASEP with periodic initial conditions, deriving the limiting kernel and connecting it to last passage percolation and random matrix theory.

Contribution

It provides a self-contained derivation of the limiting kernel for TASEP with periodic initial conditions, extending previous results and clarifying connections to other models.

Findings

Derived the kernel in the scaling limit for periodic initial conditions

Connected TASEP fluctuations to last passage percolation and random matrices

Provided a comprehensive derivation previously announced in a letter

Abstract

We consider the joint distributions of particle positions for the continuous time totally asymmetric simple exclusion process (TASEP). They are expressed as Fredholm determinants with a kernel defining a signed determinantal point process. We then consider certain periodic initial conditions and determine the kernel in the scaling limit. This result has been announced first in a letter by one of us and here we provide a self-contained derivation. Connections to last passage directed percolation and random matrices are also briefly discussed.