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 fourmomenta. 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 cutoff), so that lower energy observations may provide strong constraints on the role of a fluctuating space-time structure.
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