Testing Theoretical Models for the Higher-Order Moments of Dark Halo Distribution

Using high--resolution N--body simulations, we test two theoretical models, based either on spherical or on ellipsoidal collapse model, for the higher--order moments of the dark matter halo distribution in CDM models. We find that a theoretical model based on spherical collapse describes accurately the simulated counts--in--cells moments for haloes of several mass ranges. It appears that the model using ellipsoidal collapse instead of spherical collapse in defining dark haloes is unable to improve the models for the higher--order moments of halo distribution, for haloes much smaller than $M^*$ (the mass scale on which the fluctuation of the density field has a rms about 1). Both models are particularly accurate for the descendants of haloes selected at high redshift, and so are quite useful in interpreting the high--order moments of galaxies. As an application we use the theoretical model to predict the higher--order moments of the Lyman break galaxies observed at $z\approx 3$ and their descendants at lower redshifts.