Mean value and fluctuations in a model of diffusion in porous media.

We consider a stochastic model for the diffusion in a porous media. For a case where the average satisfies an anomalous diffusion equation, we investigate the behavior of the realizations around the mean value. The most relevant result of our work is that, although the concentration corresponding to each realization diffuses normally for large times, it experiences large deviations from the mean value during intermediate times. As a consequence, the experimental measurements will always depart from the average value of the realizations (with respect to the stochastic process) for unpredictable times.