Please use this identifier to cite or link to this item: http://buratest.brunel.ac.uk/handle/2438/4550
Full metadata record
DC FieldValueLanguage
dc.contributor.authorAkemann, G-
dc.contributor.authorKieburg, M-
dc.contributor.authorPhillips, M J-
dc.date.accessioned2010-10-04T14:00:50Z-
dc.date.available2010-10-04T14:00:50Z-
dc.date.issued2010-
dc.identifier.citationJournal of Physics A: Mathematical and Theoretical, 43 (2010) 375207en
dc.identifier.issn1751-8113-
dc.identifier.urihttp://bura.brunel.ac.uk/handle/2438/4550-
dc.description.abstractWe apply the method of skew-orthogonal polynomials (SOP) in the complex plane to asymmetric random matrices with real elements, belonging to two different classes. Explicit integral representations valid for arbitrary weight functions are derived for the SOP and for their Cauchy transforms, given as expectation values of traces and determinants or their inverses, respectively. Our proof uses the fact that the joint probability distribution function for all combinations of real eigenvalues and complex conjugate eigenvalue pairs can be written as a product. Examples for the SOP are given in terms of Laguerre polynomials for the chiral ensemble (also called the non-Hermitian real Wishart-Laguerre ensemble), both without and with the insertion of characteristic polynomials. Such characteristic polynomials play the role of mass terms in applications to complex Dirac spectra in field theory. In addition, for the elliptic real Ginibre ensemble we recover the SOP of Forrester and Nagao in terms of Hermite polynomials.en
dc.language.isoenen
dc.publisherIoPen
dc.subjectSkew-orthogonal Laguerre polynomialsen
dc.subjectReal asymmetric random matricesen
dc.subjectCharacteristic polynomialsen
dc.subjectCauchy transformen
dc.titleSkew-orthogonal Laguerre polynomials for chiral real asymmetric random matricesen
dc.typeResearch Paperen
Appears in Collections:Dept of Mathematics Research Papers
Mathematical Sciences

Files in This Item:
File Description SizeFormat 
Fulltext.pdf213.58 kBAdobe PDFView/Open


Items in BURA are protected by copyright, with all rights reserved, unless otherwise indicated.