Singular statistics

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2000-12-04

arxiv.org/abs/nlin/0012003v1

Nonlinear Sciences

Chaotic Dynamics

32 pages, 4 figures, submitted to Phys. Rev. E, 2000

Scientific paper

10.1103/PhysRevE.63.036206

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.

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