  We study the anisotropy signature which is expected if the sources of ultra
high energy, >10^{19} eV, cosmic-rays (UHECRs) are extragalactic and trace the
large scale distribution of luminous matter. Using the PSCz galaxy catalog as a
tracer of the large scale structure (LSS), we derive the expected all sky
angular distribution of the UHECR intensity. We define a statistic, that
measures the correlation between the predicted and observed UHECR arrival
direction distributions, and show that it is more sensitive to the expected
anisotropy signature than the power spectrum and the two point correlation
function. The distribution of the correlation statistic is not sensitive to the
unknown redshift evolution of UHECR source density and to the unknown strength
and structure of inter-galactic magnetic fields. We show, using this statistic,
that recently published >5.7x10^{19} eV Auger data are inconsistent with
isotropy at ~98% CL, and consistent with a source distribution that traces LSS,
with some preference to a source distribution that is biased with respect to
the galaxy distribution. The anisotropy signature should be detectable also at
lower energy, >4x10^{19} eV. A few fold increase of the Auger exposure is
likely to increase the significance to >99% CL, but not to >99.9% CL (unless
the UHECR source density is comparable or larger than that of galaxies). In
order to distinguish between different bias models, the systematic uncertainty
in the absolute energy calibration of the experiments should be reduced to well
below the current ~25%.
