  We calculate the rate at which dark matter halos merge to form higher mass
systems. Two complementary derivations using Press-Schechter theory are given,
both of which result in the same equation for the formation rate. First, a
derivation using the properties of the Brownian random walks within the
framework of Press-Schechter theory is presented. We then use Bayes' theorem to
obtain the same result from the standard Press-Schechter mass function. The
rate obtained is shown to be in good agreement with results from Monte-Carlo
and N-body simulations. We illustrate the usefulness of this formula by
calculating the expected cosmological evolution in the rate of star formation
that is due to short-lived, merger-induced starbursts. The calculated evolution
is well-matched to the observed evolution in ultraviolet luminosity density, in
contrast to the lower rates of evolution that are derived from semi-analytic
models that do not include a dominant contribution from starbursts. Hence we
suggest that the bulk of the observed ultraviolet starlight at z > 1 arises
from short-lived, merger-induced starbursts. Finally, we show that a simple
merging-halo model can also account for the bulk of the observed evolution in
the comoving quasar space density.
