Singular statistics

Eugène Bogomolny, Ulrich Gerland, Charles Schmit

Research output: Contribution to journalArticlepeer-review

45 Scopus citations


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.

Original languageEnglish
JournalPhysical Review E - Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics
Issue number3
StatePublished - 2001
Externally publishedYes


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