  In this work we establish a link between two different phenomena that were
studied in a large and growing number of biological, composite and soft media:
the diffusion in compartmentalized environment and the Brownian yet
non-Gaussian diffusion that exhibits linear growth of the mean square
displacement joined by the exponential shape of the positional probability
density. We explore a microscopic model that gives rise to transient
confinement, similar to the one observed for hop-diffusion on top of a cellular
membrane. The compartmentalization of the media is achieved by introducing
randomly placed, identical barriers. Using this model of a heterogeneous medium
we derive a general class of random walks with simple jump rules that are
dictated by the geometry of the compartments. Exponential decay of positional
probability density is observed and we also quantify the significant decrease
of the long time diffusion constant. Our results suggest that the observed
exponential decay is a general feature of the transient regime in
compartmentalized media.
