  The clustering of matter on cosmological scales is an essential probe for
studying the physical origin and composition of our Universe. To date, most of
the direct studies have focused on shear-shear weak lensing correlations, but
it is also possible to extract the dark matter clustering by combining
galaxy-clustering and galaxy-galaxy-lensing measurements. In this study we
develop a method that can constrain the dark matter correlation function from
galaxy clustering and galaxy-galaxy-lensing measurements, by focusing on the
correlation coefficient between the galaxy and matter overdensity fields. To
generate a mock galaxy catalogue for testing purposes, we use the Halo
Occupation Distribution approach applied to a large ensemble of N-body
simulations to model pre-existing SDSS Luminous Red Galaxy sample observations.
Using this mock catalogue, we show that a direct comparison between the excess
surface mass density measured by lensing and its corresponding galaxy
clustering quantity is not optimal. We develop a new statistic that suppresses
the small-scale contributions to these observations and show that this new
statistic leads to a cross-correlation coefficient that is within a few percent
of unity down to 5 Mpc/h. Furthermore, the residual incoherence between the
galaxy and matter fields can be explained using a theoretical model for
scale-dependent bias, giving us a final estimator that is unbiased to within
1%. We also perform a comprehensive study of other physical effects that can
affect the analysis, such as redshift space distortions and differences in
radial windows between galaxy clustering and weak lensing observations. We
apply the method to a range of cosmological models and show the viability of
our new statistic to distinguish between cosmological models.
