  In a survey disclosure model, we consider an additive noise privacy mechanism
and study the trade-off between privacy guarantees and statistical utility.
Privacy is approached from two different but complementary viewpoints:
information and estimation theoretic. Motivated by the performance of principal
component analysis, statistical utility is measured via the spectral gap of a
certain covariance matrix. This formulation and its motivation rely on
classical results from random matrix theory. We prove some properties of this
statistical utility function and discuss a simple numerical method to evaluate
it.
