  We present new formulae for the mass functions of the clusters and the
isolated clusters with non Gaussian initial conditions. For this study, we
adopt the Extended Zel'dovich (EZL) model as a basic framework, focusing on the
case of primordial non-Gaussianity of the local type whose degree is quantified
by a single parameter $f_{nl}$. By making a quantitative comparison with the
N-body results, we first demonstrate that the EZL formula with the constant
values of three fitting parameters still works remarkably well for the local
$f_{nl}$ case. We also modify the EZL formula to find an analytic expression
for the mass function of isolated clusters which turns out to have only one
fitting parameter other than the overall normalization factor and showed that
the modified EZL formula with a constant value of the fitting parameter matches
excellently the N-body results with various values of $f_{nl}$ at various
redshifts. Given the simplicity of the generalized EZL formulae and their good
agreements with the numerical results, we finally conclude that the EZL mass
functions of the massive clusters and isolated clusters should be useful as an
analytic guideline to constrain the scale dependence of the primordial
non-Gaussianity of the local type.

Cosmology and Nongalactic Astrophysics