  Most current models of Lorentz symmetry violation (LSV) at the Planck scale
involve power-like extrapolations of the Lorentz-beaking term down to
accelerator and even much lower energies. It is therefore assumed that no
intermediate energy scale alters this behaviour. But this is not the only
possible scenario: a more sophisticate energy-dependence is possible, and would
even be natural, involving significant effective thresholds at intermediate
energies. Such thresholds may exist between the Planck scale and the highest
cosmic-ray energies, or between ultra-high cosmic-ray energies and the TeV
scale, leading to interesting scenarios. In many cases, experimental
predictions of LSV patterns can be dramatically modified and space experiments
become necessary irrespective of AUGER results. By combining both kinds of
experiments, future results of cosmic-ray observations will hopefully be able
to test, for a large family of models involving various patterns of
Planck-scale physics, the possible existence of an absolute local rest frame in
the real world.
