  We study the parametric wave interaction in qua- dratic nonlinear media with
randomized distribution of the ferroelectric domains. In particular, we discuss
properties of second and cascaded third harmonic generation.
  We derive analytical formulas describing emission properties of the second
and third harmonics in the presence of domain disorder and show that the latter
process is governed by the characteristics of the constituent processes, i.e.
second harmonic generation and sum frequency mixing. We demonstrate the role of
randomness on various second and third harmonic generation regimes such as
Raman-Nath and \v{C}erenkov nonlinear diffraction. We show that the
randomness-induced incoherence in the wave interaction leads to deterioration
of conversion efficiency and angular spreading of harmonic generated in the
processes relying on transverse phase matching such as Raman-Nath. On the other
hand forward and \v{C}erenkov frequency generation are basically insensitive to
the domain randomness.
