Anisotropic KPZ growth in 2+1 dimensions: fluctuations and covariance structure

TL;DR

This paper investigates a 2+1 dimensional anisotropic KPZ growth model, revealing Gaussian fluctuations on a logarithmic scale and a correlation structure akin to a massless field, advancing understanding of stochastic surface growth.

Contribution

It provides new insights into the fluctuation behavior and correlation structure of anisotropic KPZ growth in higher dimensions, specifically in 2+1 dimensions.

Findings

Surface fluctuations are asymptotically Gaussian on a sqrt(ln(t)) scale.

Correlation structure is asymptotically described by the massless field.

Results enhance understanding of stochastic growth in anisotropic KPZ class.

Abstract

In [arXiv:0804.3035] we studied an interacting particle system which can be also interpreted as a stochastic growth model. This model belongs to the anisotropic KPZ class in 2+1 dimensions. In this paper we present the results that are relevant from the perspective of stochastic growth models, in particular: (a) the surface fluctuations are asymptotically Gaussian on a sqrt(ln(t)) scale and (b) the correlation structure of the surface is asymptotically given by the massless field.