TY - JOUR
T1 - Singular statistics
AU - Bogomolny, Eugène
AU - Gerland, Ulrich
AU - Schmit, Charles
PY - 2001
Y1 - 2001
N2 - 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.
AB - 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.
UR - http://www.scopus.com/inward/record.url?scp=0035275690&partnerID=8YFLogxK
U2 - 10.1103/PhysRevE.63.036206
DO - 10.1103/PhysRevE.63.036206
M3 - Article
AN - SCOPUS:0035275690
SN - 1063-651X
VL - 63
JO - Physical Review E - Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics
JF - Physical Review E - Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics
IS - 3
ER -