期刊
PROBABILITY THEORY AND RELATED FIELDS
卷 163, 期 1-2, 页码 61-87出版社
SPRINGER HEIDELBERG
DOI: 10.1007/s00440-014-0587-3
关键词
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资金
- NSF [PHY-1104596]
- Weston Visiting Professorship at the Weizmann Institute of Science
- von Neumann Visiting Professorship at the Princeton Institute for Advanced Study
- Direct For Mathematical & Physical Scien
- Division Of Physics [1104596] Funding Source: National Science Foundation
We consider the distribution of the values at real points of random functions which belong to the Herglotz-Pick (HP) class of analytic mappings of the upper half plane into itself. It is shown that under mild stationarity assumptions the individual values of HP functions with singular spectra have a Cauchy type distribution. The statement applies to the diagonal matrix elements of random operators, and holds regardless of the presence or not of level repulsion, i.e. applies to both random matrix and Poisson-type spectra.
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