The Weak Lensing Peak Statistics in the Mocks by the
  inverse-Gaussianization Method
  We apply the inverse-Gaussianization method proposed in
\citealt{arXiv:1607.05007} to fast produce weak lensing convergence maps and
investigate the peak statistics, including the peak height counts and peak
steepness counts, in these mocks. We find that the distribution of peak height
and steepness is in good agreement with the simulation. The difference is
$\lesssim 20\%$ for these peak statistics in the maps at source redshift
$z_s=1$. Besides, the loss of off-diagonal elements in peak covariance
motivates us to consider the super sample variance in weak lensing peak
statistics. We propose correction methods to effectively recover the
(anti-)correlation among different bins by adding scatters in the mean value of
these mocks. Finally, as an example of the application, we adopt the improved
inverse-Gaussianization method with the above improvement to fast generate
40,000 mocks to calculate precision matrices between the power spectrum and
peak statistics.
