• Corpus ID: 245906102

Furstenberg Theory of Mixed Random-Quasiperiodic Cocycles

@inproceedings{Cai2022FurstenbergTO,
  title={Furstenberg Theory of Mixed Random-Quasiperiodic Cocycles},
  author={Ao Cai and Pedro Duarte and Silvius Klein},
  year={2022}
}
We derive a criterion for the positivity of the maximal Lyapunov exponent of generic mixed random-quasiperiodic linear cocycles, a model introduced in a previous work. This result is applicable to cocycles corresponding to Schrödinger operators with randomly perturbed quasiperiodic potentials. Moreover, we establish an average uniform convergence to the Lyapunov exponent in the Oseledets theorem. 

Positivity of the Lyapunov exponent for analytic quasiperiodic operators with arbitrary finite-valued background

. We study lower bounds on the Lyapunov exponent associated with one-frequency quasiperiodic Schr¨odinger operators with an added finite valued background potential. We prove that, for sufficiently

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