Slow decorrelations in KPZ growth

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.