  We develop a new statistical method to reanalyse angular correlations between
background QSOs and foreground galaxies that are supposed to be a consequence
of dark matter inhomogeneities acting as weak gravitational lenses. The method
is based on a weighted average over the galaxy positions and is optimized to
distinguish between a random distribution of galaxies around QSOs and a
distribution which follows an assumed QSO-galaxy two-point correlation
function, by choosing an appropriate weight function. With simulations we
demonstrate that this weighted average is slightly more significant than
Spearman's rank-order test which was used in previous investigations. In
particular, the advantages of the weighted average show up if the two-point
correlation function is weak. We then reanalyze the correlation between
high-redshift 1-Jansky QSOs and IRAS galaxies, taken from the IRAS Faint Source
Catalog; these samples were analyzed previously using Spearman's rank-order
test. In agreement with the previous work, we find moderate to strong
correlations between these two samples; considering the angular two-point
correlation function of these samples, we find a typical scale of order $5'$
from which most of the correlation signal derives. However, the statistical
significance of the correlation changes with the redshift slices of the QSO
sample one considers. Comparing with simple theoretical estimates of the
expected correlation, we find that the signal we derive is considerably
stronger than expected. On the other hand, recent direct verifications of the
overdensity of matter in the line-of-sight to high-redshift radio QSOs obtained
from the shear field around these sources, indicates that the observed
association can be attributed to a gravitational lens effect.

Astrophysics