  We consider the statistical distribution of zeros of random meromorphic
functions whose poles are independent random variables. It is demonstrated that
correlation functions of these zeros can be computed analytically and explicit
calculations are performed for the 2-point correlation function. This problem
naturally appears in e.g. rank-one perturbation of an integrable Hamiltonian
and, in particular, when a $\delta$-function potential is added to an
integrable billiard.
