  We report on the clustering properties of Lyman-break galaxies (LBGs) at z~3.
The correlation length of flux-limited samples of LBGs depends on their
rest-frame ultraviolet (UV) luminosity at lambda ~1700 Angstrom, with fainter
galaxies being less strongly clustered in space. It decreases by a factor ~3
over the range of limiting magnitudes that we have probed, namely 25<R<27,
suggesting that fainter samples include galaxies with smaller mass. We find
that: 1) the clustering strength of LBGs follows, within the errors, the same
scaling law with the volume density predicted for cold dark matter (CDM) halos;
2) the scaling law predicted for the galaxies using the halos mass spectrum and
a number of models for the relationship that maps the halos' mass into the
galaxies' UV luminosity depends only on how tightly mass and UV luminosity
correlate, but is otherwise insensitive to the details of the models. These
results provide additional evidence that the strong spatial clustering of LBGs
is due to galaxy biasing, supporting biased galaxy formation and gravitational
instability as the primary mechanism for the formation of structure. We also
find that 1) a scale invariant relationship between mass and UV luminosity
(e.g. a power law) is not supported, suggesting that the properties of star
formation of galaxies change along the mass spectrum of the observed LBGs; 2)
the scatter of the UV luminosity of LBGs of given mass must be relatively small
for massive LBGs, suggesting that the mass is an important parameter in
regulating the activity of star formation in these systems, and that the
fraction of massive halos at z~3 that are not observed in UV-selected surveys
is not large.
