Cosmological Constraints From Weak Lensing Peak Statistics With CFHT
  Stripe 82 Survey
  We derived constraints on cosmological parameters using weak lensing peak
statistics measured on the $\sim130~{\rm deg}^2$ of the Canada-France-Hawaii
Telescope Stripe 82 Survey (CS82). This analysis demonstrates the feasibility
of using peak statistics in cosmological studies. For our measurements, we
considered peaks with signal-to-noise ratio in the range of $\nu=[3,6]$. For a
flat $\Lambda$CDM model with only $(\Omega_{\rm m}, \sigma_8)$ as free
parameters, we constrained the parameters of the following relation
$\Sigma_8=\sigma_8(\Omega_{\rm m}/0.27)^{\alpha}$ to be: $\Sigma_8=0.82 \pm
0.03 $ and $\alpha=0.43\pm 0.02$. The $\alpha$ value found is considerably
smaller than the one measured in two-point and three-point cosmic shear
correlation analyses, showing a significant complement of peak statistics to
standard weak lensing cosmological studies. The derived constraints on
$(\Omega_{\rm m}, \sigma_8)$ are fully consistent with the ones from either
WMAP9 or Planck. From the weak lensing peak abundances alone, we obtained
marginalised mean values of $\Omega_{\rm m}=0.38^{+0.27}_{-0.24}$ and
$\sigma_8=0.81\pm 0.26$. Finally, we also explored the potential of using weak
lensing peak statistics to constrain the mass-concentration relation of dark
matter halos simultaneously with cosmological parameters.
