Universal Distributions for Growth Processes in 1+1 Dimensions and Random Matrices

TL;DR

This paper develops a scaling theory for one-dimensional KPZ growth, identifying three universal distributions for shape fluctuations, computed via Gaussian random matrix partition functions, advancing understanding of growth processes and their universal properties.

Contribution

It introduces a new scaling theory for KPZ growth in 1+1 dimensions and identifies three universal fluctuation distributions based on Gaussian random matrices.

Findings

Identified three universal shape fluctuation distributions.

Connected fluctuation distributions to Gaussian random matrix partition functions.

Provided a detailed scaling framework for KPZ growth in 1D.

Abstract

We develop a scaling theory for KPZ growth in one dimension by a detailed study of the polynuclear growth (PNG) model. In particular, we identify three universal distributions for shape fluctuations and their dependence on the macroscopic shape. These distribution functions are computed using the partition function of Gaussian random matrices in a cosine potential.