# Universality of the GOE Tracy-Widom distribution for TASEP with arbitrary particle density

## TL;DR

This paper proves that the fluctuations of the height function in TASEP with any fixed particle density follow the GOE Tracy-Widom distribution, demonstrating universality across various initial conditions and slopes.

## Contribution

It establishes the universality of GOE Tracy-Widom fluctuations for TASEP with arbitrary particle density and initial conditions, extending previous results.

## Key findings

- GOE Tracy-Widom distribution describes height fluctuations
- Universality holds for arbitrary particle density rho
- Results apply to point-to-line last passage percolation with any slope

## Abstract

We consider TASEP in continuous time with non-random initial conditions and arbitrary fixed density of particles rho. We show GOE Tracy-Widom universality of the one-point fluctuations of the associated height function. The result phrased in last passage percolation language is the universality for the point-to-line problem where the line has an arbitrary slope.