On inhomogeneous polynuclear growth

TL;DR

This paper investigates the inhomogeneous geometric polynuclear growth model, deriving its distribution functions and analyzing asymptotics in the KPZ limit, thereby extending understanding of multi-time distributions in the KPZ universality class.

Contribution

It introduces a method to derive distribution functions for the inhomogeneous geometric polynuclear growth model in multiple directions and analyzes their asymptotics in the KPZ scaling limit.

Findings

Derived distribution functions in space-like and time-like directions.

Extended single-time distributions to two-time distributions in KPZ class.

Analyzed asymptotics of two-time distribution in the KPZ-scaling limit.

Abstract

This article studies the inhomogeneous geometric polynuclear growth model, the distribution of which is related to Schur functions. We explain a method to derive its distribution functions in both space-like and time-like directions, focusing on the two-time distribution. Asymptotics of the two-time distribution in the KPZ-scaling limit is then considered, extending to two times several single-time distributions in the KPZ universality class.