Geodesic
Positivity of Lyapunov exponents for Anderson-type models on two coupled strings
Electronic journal of differential equations, Tome 2007 (2007)
We 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.
Classification : 82B44, 47B80, 81Q10
Keywords: random operators, Anderson model, Lyapunov exponents 
@article{EJDE_2007__2007__a44,
     author = {Boumaza,  Hakim and Stolz,  G\"unter},
     title = {Positivity of {Lyapunov} exponents for {Anderson-type} models on two coupled strings},
     journal = {Electronic journal of differential equations},
     year = {2007},
     volume = {2007},
     zbl = {1187.82055},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/EJDE_2007__2007__a44/}
}
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%A Stolz,  Günter
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%F EJDE_2007__2007__a44
Boumaza,  Hakim; Stolz,  Günter. Positivity of Lyapunov exponents for Anderson-type models on two coupled strings. Electronic journal of differential equations, Tome 2007 (2007). http://geodesic.mathdoc.fr/item/EJDE_2007__2007__a44/