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We calculate the kurtosis of a large-scale density field which has undergoneweakly non-linear gravitational evolution from arbitrary non-Gaussian initialconditions. It is well known that the weakly evolved {\twelveit skewness} isequal to its initial value plus the term induced by gravity, which scales withthe rms density fluctuation in precisely the same way as for Gaussian initialconditions. As in the case of skewness, the evolved {\twelveit kurtosis} isequal to its initial value plus the contribution induced by gravity. Thescaling of this induced contribution, however, turns out to be qualitativelydifferent for Gaussian versus non-Gaussian initial conditions. Therefore,measurements of the kurtosis can serve as a powerful discriminating testbetween the hypotheses of Gaussian and non-Gaussian nature of primordialdensity fluctuations.Comment: uuencoded compressed tar file including postscript text (17 pages)  and 2 postscript figures, submitted to MNRA

Kurtosis in large-scale structure as a constraint on non-Gaussian initial conditions