  We calculate the effect of two kinds of randomness on the hopping of an
excitation through a nearly regular Rydberg gas. We present calculations for
how fast the excitation can hop away from its starting position for different
dimensional lattices and for different levels of randomness. We also examine
the asymptotic in time final position of the excitation to determine whether or
not the excitation can be localized. The one dimensional system is an example
of Anderson localization where the randomness is in the off-diagonal elements
although the long-range nature of the interaction leads to non-exponential
decay with distance. The two dimensional square lattice shows a mixture of
extended and localized states for large randomness while there is no visible
sign of localized states for weak randomness. The three dimensional cubic
lattice has few localized states even for strong randomness.
