On the Spatial Distribution of Dark Matter Halos

We study the spatial distribution of dark matter halos in the Universe, in terms of their number density contrast, which is related to the underlying dark matter fluctuation via a non-local and non-linear random bias field. The description of the matter dynamics is simplified by adopting the `truncated' Zel'dovich approximation to obtain both analytical results and simulated maps. The halo number density field in our maps and its probability distribution function reproduce with excellent accuracy those of halos obtained from a high-resolution N-body code with the same initial conditions. Our non-linear and non-local bias prescription matches the N-body halo distribution better than any Eulerian linear and local bias.