Magnetic horizons of UHECR sources and the GZK feature

We study the effect of random extra-galactic magnetic fields on the propagation of protons of energy larger than 10 eV. We show that for reasonable field values (in the 100 nG range) the transition between diffusive and ballistic regimes occurs in the same energy range as the GZK cutoff (a few 10 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 reduced.