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The number density of local maxima of weak lensing field, referred to asweak-lensing peak counts, can be used as a cosmological probe. However, itsrelevant cosmological information is still unclear. We study the relationshipbetween the peak counts and other statistics in weak lensing field by using1000 ray-tracing simulations. We construct a local transformation of lensingfield $\cal K$ to a new Gaussian field $y$, named local-Gaussianizedtransformation. We calibrate the transformation with numerical simulations sothat the one-point distribution and the power spectrum of $\cal K$ can bereproduced from a single Gaussian field $y$ and monotonic relation between $y$and $\cal K$. Therefore, the correct information of two-point clustering andany order of moments in weak lensing field should be preserved underlocal-Gaussianized transformation. We then examine if local-Gaussianizedtransformation can predict weak-lensing peak counts in simulations. Thelocal-Gaussianized transformation is insufficient to explain weak-lensing peakcounts in the absence of shape noise. The prediction by local-Gaussianizedtransformation underestimates the simulated peak counts with a level of$\sim20-30\%$ over a wide range of peak heights. Local-Gaussianizedtransformation can predict the weak-lensing peak counts with a $\sim10\%$accuracy in the presence of shape noise. Our analyses suggest that thecosmological information beyond power spectrum and its moments would benecessary to predict the weak-lensing peak counts with a percent-levelaccuracy, which is an expected statistical uncertainty in upcoming wide-fieldgalaxy surveys.

Statistical connection of peak counts to power spectrum and moments in weak lensing field