  We investigate the weak lensing signature of primordial non-Gaussianities of
the local type by constraining the magnitude of the weak convergence bi- and
trispectra expected for the EUCLID weak lensing survey. Starting from
expressions for the weak convergence spectra, bispectra and trispectra, whose
relative magnitudes we investigate as a function of scale, we compute their
respective signal to noise ratios by relating the polyspectra's amplitude to
their Gaussian covariance using a Monte-Carlo technique for carrying out the
configuration space integrations. In computing the Fisher-matrix on the
non-Gaussianity parameters f_nl, g_nl and tau_nl with a very similar technique,
we can derive Bayesian evidences for a violation of the Suyama-Yamaguchi
relation tau_nl>=(6 f_nl/5)^2 as a function of the true f_nl and tau_nl-values
and show that the relation can be probed down to levels of f_nl~10^2 and
tau_nl~10^5. In a related study, we derive analytical expressions for the
probability density that the SY-relation is exactly fulfilled, as required by
models in which any one field generates the perturbations. We conclude with an
outlook on the levels of non-Gaussianity that can be probed with tomographic
lensing surveys.
