We consider continuous-time random walk models described by arbitrary sojourn
time probability density functions. We find a general expression for the
distribution of time-averaged observables for such systems, generalizing some
recent results presented in the literature. For the case where sojourn times
are identically distributed independent random variables, our results shed some
light on the recently proposed transitions between ergodic and weakly
nonergodic regimes. On the other hand, for the case of non-identical trapping
time densities over the lattice points, the distribution of time-averaged
observables reveals that such systems are typically nonergodic, in agreement
with some recent experimental evidences on the statistics of blinking quantum
dots. Some explicit examples are considered in detail. Our results are
independent of the lattice topology and dimensionality.Comment: 8 pages, final version to appear in PR
