t^{1/3} fluctuation around the shock of TASEP with random initial condition

TL;DR

This paper investigates the fluctuation behavior of TASEP with specific initial conditions, revealing a transition from Gaussian to t^{1/3} fluctuations around shocks, aligning with KPZ universality class predictions.

Contribution

The paper demonstrates the emergence of t^{1/3} fluctuations in TASEP with shock initial conditions, extending understanding of fluctuation regimes beyond classical Gaussian behavior.

Findings

Identification of t^{1/3} fluctuations around shocks

Extension of KPZ universality class results

Clarification of fluctuation transition mechanisms

Abstract

The totally asymmetric exclusion process (TASEP) is one of the solvable models in the KPZ universality class. When TASEP starts with the product Bernoulli measure with a smaller density on the left of the origin, it presents shocks in the evolution. For a long time, it has been known that fluctuations are the product of Gaussians on the scale t^{1/2} due to initial randomness. In this paper, we will describe how to see the t^{1/3} fluctuations for these initial conditions.