Positivity of Lyapunov exponents for Anderson-type models on two coupled strings

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dc.contributor.authorBoumaza, Hakim
dc.contributor.authorStolz, Gunter
dc.date.accessioned2021-08-05T16:13:32Z
dc.date.available2021-08-05T16:13:32Z
dc.date.issued2007-03-20
dc.description.abstractWe study two models of Anderson-type random operators on two deterministically coupled continuous strings. Each model is associated with independent, identically distributed four-by-four symplectic transfer matrices, which describe the asymptotics of solutions. In each case we use a criterion by Gol'dsheid and Margulis (i.e. Zariski denseness of the group generated by the transfer matrices in the group of symplectic matrices) to prove positivity of both leading Lyapunov exponents for most energies. In each case this implies almost sure absence of absolutely continuous spectrum (at all energies in the first model and for sufficiently large energies in the second model). The methods used allow for singularly distributed random parameters, including Bernoulli distributions.
dc.description.departmentMathematics
dc.formatText
dc.format.extent18 pages
dc.format.medium1 file (.pdf)
dc.identifier.citationBoumaza, H., & Stolz, G. (2007). Positivity of Lyapunov exponents for Anderson-type models on two coupled strings. <i>Electronic Journal of Differential Equations, 2007</i>(47), pp. 1-18.
dc.identifier.issn1072-6691
dc.identifier.urihttps://hdl.handle.net/10877/14208
dc.language.isoen
dc.publisherTexas State University-San Marcos, Department of Mathematics
dc.rightsAttribution 4.0 International
dc.rights.urihttps://creativecommons.org/licenses/by/4.0/
dc.sourceElectronic Journal of Differential Equations, 2007, San Marcos, Texas: Texas State University-San Marcos and University of North Texas.
dc.subjectRandom operators
dc.subjectAnderson model
dc.subjectLyapunov exponents
dc.titlePositivity of Lyapunov exponents for Anderson-type models on two coupled strings
dc.typeArticle

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