  The intimate geometry of space-time is expected to suffer stochastic
fluctuations as a result of quantum gravitational effects. These fluctuations
may induce observable consequences on the propagation of high energy particles
over large distances, so that the strength and the characteristics of these
fluctuations may be constrained, mainly in the range of energies of interest
for cosmic ray physics. While invoked as a possible explanation for the
detection of the puzzling cosmic rays with energies in excess of the threshold
for photopion production (the so-called super-GZK particles), we demonstrate
here that lower energy observations may provide strong constraints on the role
of a fluctuating space-time structure.
