  Primordial black holes (PBHs) are black holes that might have formed in high
density regions in the early universe. The presence of local-type
non-Gaussianity can lead to large-scale fluctuations in the PBH formation rate.
If PBHs make up a non-negligible fraction of dark matter, these fluctuations
can appear as isocurvature modes, and be used to constrain the amplitude of
non-Gaussianity. Assuming that the parameters of non-Gaussianity are constant
over all scales, we build upon the results of previous work by extending the
calculation to include peaks theory and making use of the compaction $C$ for
the formation criteria, accounting for non-linearities between $C$ and the
curvature perturbation $\zeta$. For quadratic models of non-Gaussianity, our
updated calculation gives constraints that are largely unaltered compared to
those previously found, while for cubic models the constraints worsen
significantly. In case all of the DM is made up of PBHs, the parameters of
non-Gaussianity are $-2.9\cdot10^{-4}<f<3.8\cdot10^{-4}$ and
$-1.5\cdot10^{-3}<g<1.9\cdot10^{-3}$ for quadratic and cubic models
respectively.
