  We extend the method of rescaled Ward identities of Ameur-Kang-Makarov to
study the distribution of eigenvalues close to a bulk singularity, i.e. a point
in the interior of the droplet where the density of the classical equilibrium
measure vanishes. We prove results to the effect that a certain "dominant part"
of the Taylor expansion determines the microscopic properties near a bulk
singularity. A description of the distribution is given in terms of a special
entire function, which depends on the nature of the singularity (a
Mittag-Leffler function in the case of a rotationally symmetric singularity).
