  The continuous-time random walk (CTRW) model is useful for alleviating the
computational burden of simulating diffusion in actual media. In principle,
isotropic CTRW only requires knowledge of the step-size, $P_l$, and
waiting-time, $P_t$, distributions of the random walk in the medium and it then
generates presumably equivalent walks in free space, which are much faster.
Here we test the usefulness of CTRW to modelling diffusion of finite-size
particles in porous medium generated by loose granular packs. This is done by
first simulating the diffusion process in a model porous medium of mean
coordination number, which corresponds to marginal rigidity (the loosest
possible structure), computing the resulting distributions $P_l$ and $P_t$ as
functions of the particle size, and then using these as input for a free space
CTRW. The CTRW walks are then compared to the ones simulated in the actual
media.
  In particular, we study the normal-to-anomalous transition of the diffusion
as a function of increasing particle size. We find that, given the same $P_l$
and $P_t$ for the simulation and the CTRW, the latter predicts incorrectly the
size at which the transition occurs. We show that the discrepancy is related to
the dependence of the effective connectivity of the porous media on the
diffusing particle size, which is not captured simply by these distributions.
  We propose a correcting modification to the CTRW model -- adding anisotropy
-- and show that it yields good agreement with the simulated diffusion process.
We also present a method to obtain $P_l$ and $P_t$ directly from the porous
sample, without having to simulate an actual diffusion process. This extends
the use of CTRW, with all its advantages, to modelling diffusion processes of
finite-size particles in such confined geometries.
