We study the spatial distribution of dark matter halos in the universe in t
erms of their number density contrast, related to the underlying dark matte
r fluctuation via a nonlocal and nonlinear bias random field. The descripti
on of the matter dynamics is simplified by adopting the "truncated" Zeldovi
ch approximation to obtain both analytical results and simulated maps. The
halo number density field in our maps and its probability distribution repr
oduce with excellent accuracy those of halos in a high-resolution N-body si
mulation 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.