Limiting distributions for a polynuclear growth model with external sources

TL;DR

This paper studies the limiting distribution functions in a polynuclear growth model with external sources, revealing when they match Tracy-Widom distributions or a new explicit distribution, and explores transitions between these distributions.

Contribution

It introduces a new explicit distribution function with zero mean and characterizes transition functions between known and new distributions in growth models.

Findings

Limiting distributions are Tracy-Widom or a new explicit function.

Transition functions are derived between different limiting distributions.

Results extend to a discrete totally asymmetric exclusion process.

Abstract

The purpose of this paper is to investigate the limiting distribution functions for a polynuclear growth model with two external sources, which was considered by Pr\"ahofer and Spohn. Depending on the strength of the sources, the limiting distribution functions are either the Tracy-Widom functions of random matrix theory, or a new explicit function which has the special property that its mean is zero. Moreover, we obtain transition functions between pairs of the above distribution functions in suitably scaled limits. There are also similar results for a discrete totally asymmetric exclusion process.