  Although we lack complete understanding of quantum aspects of gravitation, it
is usually agreed, using general arguments, that a final quantum gravity theory
will endow space and time with some (fundamental or effective) notion of
discreteness. This granular character is supposed to lie on space and time
scales of $l_P \sim 10^{-33}$ cm and $\tau_P\sim 10^{-42}$ s, respectively --
the Planck scale -- , far beyond any hope of direct assessment. Here, by
modeling displacements of particles on a discrete underlying space as Poisson
processes, we speculate on the possibility of amplifying the effects of space
discreteness (if existent) by several orders of magnitude, using the
statistical variance of correlated displacements of particles/systems with very
different masses. Although still out of reach by current technology, the
analysis presented here suggests that it may be possible to see hints of
space(time) discreteness at larger scales than one would usually expect.
