Formation rates of Dark Matter Haloes
  We derive an estimate of the rate of formation of dark matter halos per unit
volume as a function of the halo mass and redshift of formation. Analytical
estimates of the number density of dark matter halos are useful in modeling
several cosmological phenomena. We use the excursion set formalism for
computing the formation rate of dark matter halos. We use an approach that
allows us to differentiate between major and minor mergers, as this is a
pertinent issue for semi-analytic models of galaxy formation. We compute the
formation rate for the Press-Schechter and the Sheth-Tormen mass function. We
show that the formation rate computed in this manner is positive at all scales.
We comment on the Sasaki formalism where negative halo formation rates are
obtained. Our estimates compare very well with N-Body simulations for a variety
of models. We also discuss the halo survival probability and the formation
redshift distributions using our method.
