Dynamical regimes and finite time behavior in a trapped random walk: a direct iterative approach

We consider a basic one-dimensional model of diffusion which allows to obtain a diversity of diffusive regimes whose speed depends on the moments of the per-site trapping time. This model is closely related to the continuous time random walks widely studied in the literature. The model we consider lends itself to a detailed treatment, making it possible to study deviations from normality due to finite time effects.