Superdiffusivity of Asymmetric Energy Model in Dimension One and Two

TL;DR

This paper investigates the asymmetric energy model's diffusion properties in one and two dimensions, providing lower bounds and confirming divergence of the diffusion coefficient as predicted by the KPZ universality class.

Contribution

It establishes lower bounds for the diffusion coefficient of the AEM, demonstrating divergence in low dimensions, aligning with KPZ class predictions.

Findings

Diffusion coefficient diverges in 1D and 2D

Lower bounds for the diffusion coefficient are obtained

Supports the KPZ universality class behavior

Abstract

We discuss an asymmetric energy model (AEM) introduced by Giardina et al. in \cite{7}. This model is expected to belong to the KPZ class. We obtain lower bounds for the diffusion coefficient. In particular, the diffusion coefficient is diverging in dimension one and two as it is expected in the KPZ picture.