  We present a simple formalism to interpret two galaxy statistics, the UV
luminosity function and two-point correlation functions for star-forming
galaxies at z~4, 5, 6 in the context of LCDM cosmology. Both statistics are the
result of how star formation takes place in DM halos, and thus are used to
constrain how UV light depends on halo properties such as mass. The two
measures were taken from the GOODS data, thus ideal for joint analysis. The two
physical quantities we explore are the SF duty cycle, and the range of L_UV
that a halo of mass M can have (mean and variance). The former addresses the
typical duration of SF activity in halos while the latter addresses the
averaged SF history and regularity of gas inflow into these systems. We explore
various physical models consistent with data, and find the following: 1) the
typical duration of SF observed in the data is <0.4 Gyr (1 sig), 2) the
inferred scaling law between L_UV and halo mass M from the observed slope of
the LFs is roughly linear at all redshifts, and 3) L_UV for a fixed halo mass
decreases with time, implying that the SF efficiency (after dust extinction) is
higher at earlier times. We explore several physical scenarios relating star
formation to halo mass, but find that these scenarios are indistinguishable due
to the limited range of halo mass probed by our data. In order to discriminate
between different scenarios, we discuss constraining the bright-faint galaxy
cross-correlation functions and luminosity-dependence of galaxy bias.
(Abridged)
