  We present a model of anomalous diffusion consisting of an ensemble of
particles undergoing homogeneous Brownian motion except for confinement by
randomly placed reflecting boundaries. For power-law distributed compartment
sizes, we calculate exact and asymptotic values of the ensemble averaged mean
squared displacement and find that it increases subdiffusively, as either a
power or the logarithm of time. Numerical simulations show that the probability
density function of the displacement is non-Gaussian. We discuss the relevance
of the model for the analysis of single-particle tracking experiments and its
relation to other sources of subdiffusion. In particular we discuss an intimate
connection with diffusion on percolation processes.
