  It is generally expected that quantum gravity affects the structure of
space-time by introducing stochastic fluctuations in the geometry, and,
ultimately, in the measurements of four-distances and four-momenta.These
fluctuations may induce observable consequences on the propagation of ultra
high energy particles, mainly in the range of energies of interest for cosmic
ray physics, over large distances, leading to their detection or constraining
the underlying quantum gravitational structure. We argue that the detectable
effects of fluctuations may extend to energies much lower than the threshold
for proton photopion production (the so-called GZK cut-off), so that lower
energy observations may provide strong constraints on the role of a fluctuating
space-time structure.
