  Many types of point singularity have a topological index, or 'charge',
associated with them. For example the phase of a complex field depending on two
variables can either increase or decrease on making a clockwise circuit around
a simple zero, enabling the zeros to be assigned charges of plus or minus one.
In random fields we can define a correlation function for the charge-weighted
density of singularities. In many types of random fields, this correlation
function satisfies an identity which shows that the singularities 'screen' each
other perfectly: a positive singularity is surrounded by an excess of
concentration of negatives which exactly cancel its charge, and vice-versa.
This paper gives a simple and widely applicable derivation of this result. A
counterexample where screening is incomplete is also exhibited.
