$(\log t)^{2/3}$ law of the two dimensional asymmetric simple exclusion process

TL;DR

This paper proves that the diffusion coefficient in the 2D asymmetric simple exclusion process diverges following a $( ext{log } t)^{2/3}$ law, revealing new asymptotic behavior in such stochastic particle systems.

Contribution

It establishes the precise asymptotic divergence rate of the diffusion coefficient in 2D ASEP, extending to both nearest and non-nearest neighbor interactions.

Findings

Diffusion coefficient diverges as $( ext{log } t)^{2/3}$

Method applies to both nearest and non-nearest neighbor ASEP

Provides rigorous proof of asymptotic behavior

Abstract

We prove that the diffusion coefficient for the two dimensional asymmetric simple exclusion process diverges as $(\log t)^{2/3}$ to the leading order. The method applies to nearest and non-nearest neighbor asymmetric simple exclusion processes.