DC FieldValueLanguage
dc.contributor.authorChandler-Wilde, Simon N.-
dc.contributor.authorHagger, Raffael-
dc.date.accessioned2019-12-04T08:16:54Z-
dc.date.available2019-12-04T08:16:54Z-
dc.date.issued2017-
dc.identifier.citationin: Recent Trends in Operator Theory and Partial Differential Equations. Operator Theory: Advances and Applications (258): 51-78 (2017)de_DE
dc.identifier.issn0255-0156de_DE
dc.identifier.urihttp://hdl.handle.net/11420/3942-
dc.description.abstractIn this paper we study the spectrum Σ of the infinite Feinberg-Zee random hopping matrix, a tridiagonal matrix with zeros on the main diagonal and random ±1‘s on the first sub- and super-diagonals; the study of this non-selfadjoint random matrix was initiated in Feinberg and Zee (Phys. Rev. E 59 (1999), 6433-6443). Recently Hagger (Random Matrices: Theory Appl., 4 1550016 (2015)) has shown that the so-called periodic part Σπ of Σ, conjectured to be the whole of Σ and known to include the unit disk, satisfies p-1(Σπ) ⊂ Σπ for an infinite class S of monic polynomials p. In this paper we make very explicit the membership of S, in particular showing that it includes Pm(λ) = λUm-1(λ/2), for m ≥ 2, where Un(x) is the Chebychev polynomial of the second kind of degree n. We also explore implications of these inverse polynomial mappings, for example showing that Σπ is the closure of its interior, and contains the filled Julia sets of infinitely many p ∈ S, including those of Pm, this partially answering a conjecture of the second author.en
dc.language.isoende_DE
dc.publisherBirkhäuserde_DE
dc.subjectFractalde_DE
dc.subjectJacobi operatorde_DE
dc.subjectJulia setde_DE
dc.subjectNon-selfadjoint operatorde_DE
dc.subjectRandom operatorde_DE
dc.subjectSpectral theoryde_DE
dc.titleOn symmetries of the feinberg-zee random hopping matrixde_DE
dc.typeinBookde_DE
dc.type.dinibookPart-
dcterms.DCMITypeText-
tuhh.abstract.englishIn this paper we study the spectrum Σ of the infinite Feinberg-Zee random hopping matrix, a tridiagonal matrix with zeros on the main diagonal and random ±1‘s on the first sub- and super-diagonals; the study of this non-selfadjoint random matrix was initiated in Feinberg and Zee (Phys. Rev. E 59 (1999), 6433-6443). Recently Hagger (Random Matrices: Theory Appl., 4 1550016 (2015)) has shown that the so-called periodic part Σπ of Σ, conjectured to be the whole of Σ and known to include the unit disk, satisfies p-1(Σπ) ⊂ Σπ for an infinite class S of monic polynomials p. In this paper we make very explicit the membership of S, in particular showing that it includes Pm(λ) = λUm-1(λ/2), for m ≥ 2, where Un(x) is the Chebychev polynomial of the second kind of degree n. We also explore implications of these inverse polynomial mappings, for example showing that Σπ is the closure of its interior, and contains the filled Julia sets of infinitely many p ∈ S, including those of Pm, this partially answering a conjecture of the second author.de_DE
tuhh.publisher.doi10.1007/978-3-319-47079-5_3-
tuhh.publication.instituteMathematik E-10de_DE
tuhh.type.opusInBuch (Kapitel / Teil einer Monographie)-
dc.type.driverbookPart-
dc.type.casraiBook Chapter-
tuhh.container.startpage51de_DE
tuhh.container.endpage78de_DE
tuhh.relation.ispartofseriesOperator theoryde_DE
tuhh.relation.ispartofseriesnumber258de_DE
dc.identifier.scopus2-s2.0-85013921078-
datacite.resourceTypeBook Chapter-
datacite.resourceTypeGeneralText-
item.grantfulltextnone-
item.openairecristypehttp://purl.org/coar/resource_type/c_3248-
item.creatorGNDChandler-Wilde, Simon N.-
item.creatorGNDHagger, Raffael-
item.openairetypeinBook-
item.tuhhseriesidOperator theory-
item.fulltextNo Fulltext-
item.cerifentitytypePublications-
item.creatorOrcidChandler-Wilde, Simon N.-
item.creatorOrcidHagger, Raffael-
item.languageiso639-1en-
item.seriesrefOperator theory;258-
item.mappedtypeinBook-
crisitem.author.deptMathematik E-10-
crisitem.author.orcid0000-0003-0578-1283-
crisitem.author.parentorgStudiendekanat Elektrotechnik, Informatik und Mathematik-
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