Slow decorrelations in KPZ growth

TL;DR

This paper investigates the time correlation structure in KPZ class growth models, revealing slow directions with decorrelation exponents different from the typical value, impacting the understanding of surface fluctuation dynamics.

Contribution

It demonstrates that the space-time structure in KPZ models is fibred with slow directions along characteristic curves, showing decorrelation exponent 1 instead of 2/3.

Findings

Space-time is non-trivially fibred with slow directions.

Slow directions have decorrelation exponent 1.

Results for space-like paths extend to the whole space-time except along slow curves.

Abstract

For stochastic growth models in the Kardar-Parisi-Zhang (KPZ) class in 1+1 dimensions, fluctuations grow as t^{1/3} during time t and the correlation length at a fixed time scales as t^{2/3}. In this note we discuss the scale of time correlations. For a representant of the KPZ class, the polynuclear growth model, we show that the space-time is non-trivially fibred, having slow directions with decorrelation exponent equal to 1 instead of the usual 2/3. These directions are the characteristic curves of the PDE associated to the surface's slope. As a consequence, previously proven results for space-like paths will hold in the whole space-time except along the slow curves.