  We present a probabilistic theory of random walks in turbid media with
non-scattering regions. It is shown that important characteristics such as
diffusion constants, average step lengths, crossing statistics and void
spacings can be analytically predicted. The theory is validated using Monte
Carlo simulations of light transport in heterogeneous systems in the form of
random sphere packings, and good agreement is found. The role of step
correlations is discussed, and differences between unbounded and bounded
systems are investigated. Our results are relevant to the optics of
heterogeneous systems in general, and represent an important step forward in
the understanding of media with strong (fractal) heterogeneity in particular.
