The controversy whether or not the Kardar–Parisi–Zhang (KPZ) equation has an upper critical dimension (UCD) is going on for quite a long time. Some approximate integral equations for the two-point function served as an indication for the existence of a UCD, by obtaining a dimension, above...

In this paper we discuss nonlocal growth equations such as the generalization of the Kardar–Parisi–Zhang (KPZ) equation that includes long-range interactions, also known as the Nonlocal-Kardar–Parisi–Zhang (NKPZ) equation, and the nonlocal version of the molecular-beam-epitaxy (NMBE)...