  We investigate an analytic model to compute nonlinear power spectrum of dark
matter, galaxies and their cross-correlation. The model is based on
Press-Schechter halos, which cluster and have realistic dark matter profiles.
The total power spectrum is a sum of two contributions, one from correlations
betwen the halos and one from correlations within the same halo. We show that
such a model can give dark matter power spectra which match well with the
results of N-body simulations, provided that concentration parameter decreases
with the halo mass.
  Galaxy power spectrum differs from dark matter power spectrum because pair
weighted number of galaxies increases less rapidly than the halo mass, as
predicted by theoretical models and observed in clusters. In this case the
resulting power spectrum becomes a power law with the slope closed to the
observed. Such a model also predicts a later onset of nonlinear clustering
compared to the dark matter, which is needed to reconcile the CDM models with
the data. Generic prediction of this model is that bias is scale dependent and
nonmonotonic. For red or elliptical galaxies bias in power spectrum may be
scale dependent even on very large scales.
  Our predictions for galaxy-dark matter correlations, which can be observed
through the galaxy-galaxy lensing, show that these cannot be interpreted simply
as an average halo profile of a typical galaxy, because different halo masses
dominate at different scales and because larger halos host more than one
galaxy. We discuss the prospects of using cross-correlations in combination
with galaxy clustering to determine the dark matter power spectrum (ABRIDGED).
