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 two-point correlation function. This problem naturally appears in, e.g., rank-1 perturbation of an integrable Hamiltonian and, in particular, when a δ-function potential is added to an integrable billiard.

• Received 14 September 2000

DOI:https://doi.org/10.1103/PhysRevE.63.036206