In this talk, I will discuss stochastic surface growth dynamics within the
anisotropic class of the Kardar–Parisi–Zhang equation. Fluctuations of the dy-
namics are conjectured to be Gaussian in the limit of large time as if an unusual
nonlinear term in the equation does not exist. The proofs obtained recently
consider iterated scaling limits of some particle systems. I will discuss some
aspects of these results and explain the particular role of the classical central
limit theorem for the problem.