  We carry out N-body simulations of several non-Gaussian structure formation
models, including Peebles' isocurvature cold dark matter model, cosmic string
models, and a model with primordial voids. We compare the evolution of the
cluster mass function in these simulations with that predicted by a modified
version of the Press-Schechter formalism. We find that the Press-Schechter
formula can accurately fit the cluster evolution over a wide range of redshifts
for all of the models considered, with typical errors in the mass function of
less than 25%, considerably smaller than the amount by which predictions for
different models may differ. This work demonstrates that the Press-Schechter
formalism can be used to place strong model independent constraints on
non-Gaussianity in the universe.
