  We present a model to understand the redshift evolution of the UV luminosity
and stellar mass functions of Lyman Break Galaxies. Our approach is based on
the assumption that the luminosity and stellar mass of a galaxy is related to
its dark matter halo assembly and gas infall rate. Specifically, galaxies
experience a burst of star formation at the halo assembly time, followed by a
constant star formation rate, representing a secular star formation activity
sustained by steady gas accretion. Star formation from steady gas accretion is
the dominant contribution to the galaxy UV luminosity at all redshifts. The
model is calibrated by constructing a galaxy luminosity versus halo mass
relation at $z=4$ via abundance matching. After this luminosity calibration,
the model naturally fits the $z=4$ stellar mass function, and correctly
predicts the evolution of both luminosity and stellar mass functions from $z=0$
to $z=8$. While the details of star formation efficiency and feedback are
hidden within our calibrated luminosity versus halo mass relation, our study
highlights that the primary driver of galaxy evolution across cosmic time is
the build-up of dark matter halos, without the need to invoke a redshift
dependent efficiency in converting gas into stars.
