The GZK cutoff behind a Magnetized Universe

We study the effect of random extra-galactic magnetic fields on the propagation of protons of energy larger than $10^{18}$ eV. We show that for reasonable field values (in the 0.1 $\mu$G range) the transition between diffusive and ballistic regimes occurs in the same energy range as the GZK cutoff (a few $10^{19}$ eV). The usual interpretation of the flux reduction above the GZK energy in terms of a sudden reduction of the visible horizon is modified. Moreover, since the size of the diffusion sphere of a continuous source of cosmic rays is of the order of 10 Mpc, the local structure of the Universe and therefore of potential local astrophysical sources plays a dominant role in the expected spectrum. Under reasonable assumptions on the sources configurations the expected GZK cutoff is not visible.