  We study reflection and transmission of waves in a random tight-binding
system with absorption or gain for weak disorder, using a scattering matrix
formalism. Our aim is to discuss analytically the effects of absorption or gain
on the statistics of wave transport. Treating the effects of absorption or gain
exactly in the limit of no disorder, allows us to identify short- and long
lengths regimes relative to absorption- or gain lengths, where the effects of
absorption/gain on statistical properties are essentially different. In the
long-lengths regime we find that a weak absorption or a weak gain induce
identical statistical corrections in the inverse localization length, but lead
to different corrections in the mean reflection coefficient. In contrast, a
strong absorption or a strong gain strongly suppress the effect of disorder in
identical ways (to leading order), both in the localization length and in the
mean reflection coefficient.
