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, related to the underlying dark matter fluctuation via a nonlocal and nonlinear bias random field. The description of the matter dynamics is simplified by adopting the "truncated" Zeldovich approximation to obtain both analytical results and simulated maps. The halo number density field in our maps and its probability distribution reproduce with excellent accuracy those of halos in a high-resolution N-body simulation with the same initial conditions. Our nonlinear and nonlocal bias prescription matches the N-body halo distribution better than any Eulerian linear and local bias.