  The diffraction of stochastic point sets, both Bernoulli and Markov, and of
random tilings with crystallographic symmetries is investigated in rigorous
terms. In particular, we derive the diffraction spectrum of 1D random tilings,
of stochastic product tilings built from cuboids, and of planar random tilings
based on solvable dimer models, augmented by a brief outline of the diffraction
from the classical 2D Ising lattice gas. We also give a summary of the measure
theoretic approach to mathematical diffraction theory which underlies the
unique decomposition of the diffraction spectrum into its pure point, singular
continuous and absolutely continuous parts.
