On the spatial distribution of dark matter halos

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Abstract
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.

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