Statistics of Dark Matter Halos from the Excursion Set Approach

We exploit the excursion set approach in integral formulation to derive novel, accurate analytic approximations of the unconditional and conditional first crossing distributions, for random walks with uncorrelated steps and general shapes of the moving barrier; we find the corresponding approximations of the unconditional and conditional halo mass functions for Cold Dark Matter power spectra to represent very well the outcomes of state-of-the-art cosmological N-body simulations. In addition, we apply these results to derive, and confront with simulations, other quantities of interest in halo statistics, including the rates of halo formation and creation, the average halo growth history, and the halo bias. Finally, we discuss how our approach and main results change when considering random walks with correlated instead of uncorrelated steps, and Warm instead of Cold Dark Matter power spectra.