Slow decorrelations in Kardar–Parisi–Zhang growth

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 work we discuss the scale of time correlations. For a representative of the KPZ class, the polynuclear growth model, we show that the space–time is non-trivially fibered, having slow directions with decorrelation exponent equal to 1 instead of the usual 2/3. These directions are the characteristic curves of the partial differential equation associated with the surface's slope. As a consequence, previously proven results for space-like paths will hold for the whole space–time except along the slow curves.