  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 non-local and non-linear bias random 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 reproduce
with excellent accuracy those of halos in a high-resolution N-body simulation
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.
