Analytic Derivation of the Halo Mass Function from the Non-Linear Cosmic
  Density Field
  We estimate the halo mass function (HMF) by applying the excursion set
approach to the non-linear cosmic density field. Thereby, we account for the
non-Gaussianity of today's density distribution and constrain the HMF
independent of the linear collapse threshold $\delta_{\textrm{crit}}$. We
consider a spherical region as a halo, if its density today exceeds the virial
overdensity threshold $\Delta$. We model the probability distribution of the
non-linear density field by a superposition of a Gaussian and a lognormal
distribution, which we constrain with the bispectrum of density fluctuations,
predicted by the kinetic field theory description of cosmic structure
formation. Two different excursion set approaches are compared. The first
treats the density $\delta$ as an uncorrelated random walk of the smoothing
scale $R$. The second assumes $\delta(R)$ to be correlated. We find that the
resulting HMFs correspond well to the HMF found in numerical simulations if the
correlation of $\delta(R)$ is taken into account. Furthermore, the HMF depends
only weakly on the choice of the density threshold $\Delta$.
