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On the ubiquity of the Cauchy distribution in spectral problems

Author(s): Aizenman, Michael; Warzel, Simone

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dc.contributor.authorAizenman, Michael-
dc.contributor.authorWarzel, Simone-
dc.date.accessioned2019-05-30T15:59:41Z-
dc.date.available2019-05-30T15:59:41Z-
dc.date.issued2015-10en_US
dc.identifier.citationAizenman, Michael, Warzel, Simone. (2015). On the ubiquity of the Cauchy distribution in spectral problems. PROBABILITY THEORY AND RELATED FIELDS, 163 (61 - 87. doi:10.1007/s00440-014-0587-3en_US
dc.identifier.issn0178-8051-
dc.identifier.urihttp://arks.princeton.edu/ark:/88435/pr11m86-
dc.description.abstractWe 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.en_US
dc.format.extent61 - 87en_US
dc.language.isoen_USen_US
dc.relation.ispartofPROBABILITY THEORY AND RELATED FIELDSen_US
dc.rightsAuthor's manuscripten_US
dc.titleOn the ubiquity of the Cauchy distribution in spectral problemsen_US
dc.typeJournal Articleen_US
dc.identifier.doidoi:10.1007/s00440-014-0587-3-
dc.date.eissued2014-11-06en_US
dc.identifier.eissn1432-2064-
pu.type.symplectichttp://www.symplectic.co.uk/publications/atom-terms/1.0/journal-articleen_US

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