  In a gravitationally unstable universe, the structure of dark matter and
galaxies, intergalactic gas and magnetic field can have severe impact on the
propagation of ultra high energy cosmic rays (UHECR) (Ryu & Kang, this
proceedings). The possible effects include spatial confinement and directional
focusing along the supergalactic matter sheets, as well as universal
re-acceleration at large scale shock fronts, and spectral modification due to
energy dependent leakage into cosmic voids. As a result, the GZK-cutoff may be
less pronounced and occur at a higher energy, where the stochastic nature of
both acceleration and energy loss processes has to be taken into account.
