  We present a new approach to measure the mass function of dark matter halos
and to discriminate models with differing values of Omega through weak
gravitational lensing. We measure the distribution of peaks from simulated
lensing surveys and show that the lensing signal due to dark matter halos can
be detected for a wide range of peak heights. Even when the signal-to-noise is
well below the limit for detection of individual halos, projected halo
statistics can be constrained for halo masses spanning galactic to cluster
halos. The use of peak statistics relies on an analytical model of the noise
due to the intrinsic ellipticities of source galaxies. The noise model has been
shown to accurately describe simulated data for a variety of input ellipticity
distributions. We show that the measured peak distribution has distinct
signatures of gravitational lensing, and its non-Gaussian shape can be used to
distinguish models with different values of Omega. The use of peak statistics
is complementary to the measurement of field statistics, such as the
ellipticity correlation function, and possibly not susceptible to the same
systematic errors.
