Multi-point distribution of TASEP

TL;DR

This paper derives a finite-time multi-point distribution formula for continuous TASEP with general initial conditions and explores its universal limiting behavior in the KPZ class.

Contribution

It provides a new finite-time multi-point distribution formula for continuous TASEP with general initial conditions and analyzes its asymptotic limits.

Findings

Derived finite-time multi-point distribution formula for continuous TASEP.

Established universal limiting distributions for step and flat initial conditions.

Confirmed universality within the KPZ class.

Abstract

Recently Johansson and Rahman obtained the limiting multi-time distribution for the discrete polynuclear growth model, which is equivalent to a discrete TASEP model with step initial condition. In this paper, we obtain a finite time multi-point distribution formula of continuous TASEP with general initial conditions in the space-time plane. We evaluate the limit of this distribution function when the times go to infinity at the same speed for both step and flat initial conditions. These limiting distributions are expected to be universal for all the models in the Kardar-Parisi-Zhang universality class.