  We introduce a heterogeneous continuous time random walk (HCTRW) model as a
versatile analytical formalism for studying and modeling diffusion processes in
heterogeneous structures, such as porous or disordered media, multiscale or
crowded environments, weighted graphs or networks. We derive the exact form of
the propagator and investigate the effects of spatio-temporal heterogeneities
onto the diffusive dynamics via the spectral properties of the generalized
transition matrix. In particular, we show how the distribution of first passage
times changes due to local and global heterogeneities of the medium. The HCTRW
formalism offers a unified mathematical language to address various
diffusion-reaction problems, with numerous applications in material sciences,
physics, chemistry, biology, and social sciences.
