  The subject of this paper is the investigation of inflationary
non-Gaussianities of the local type with extreme value statistics of the weak
lensing convergence kappa. Specifically, we describe the influence of
inflationary non-Gaussianities parameterised by fnl and gnl on the probability
distribution p(kappa)dkappa of the smoothed convergence field with a
Gram-Charlier series, for which we compute the cumulants kappa_n of the
smoothed convergence field as a configuration space average of the weak
convergence polyspectra. We derive analytical expressions for the extreme value
distribution and show that they correspond very well to direct samples of
extreme values from the Gram-Charlier distribution. We show how the standard
Gumbel distribution for the extreme values is recovered in the limit of large
sample size. We investigate the shape and position of the extreme value
distribution for fnl- and gnl-type non-Gaussianity and quantify the dependence
on the number of available samples, leading to the inference of non-Gaussianity
parameters from observed extreme values. From the observation of single extreme
values in the EUCLID weak lensing survey is is possible to place constraints on
fnl and gnl of the order 10^2 and 10^5, respectively, while tnl can not be
constrained in a meaningful way.
