Spectral theory of extended Harper’s model and a question by Erdős and Szekeres

@article{Avila2016SpectralTO,
  title={Spectral theory of extended Harper’s model and a question by Erdős and Szekeres},
  author={Artur Avila and Svetlana Ya. Jitomirskaya and Christoph A. Marx},
  journal={Inventiones mathematicae},
  year={2016},
  volume={210},
  pages={283-339}
}
The extended Harper’s model, proposed by D.J. Thouless in 1983, generalizes the famous almost Mathieu operator, allowing for a wider range of lattice geometries (parametrized by three coupling parameters) by permitting 2D electrons to hop to both nearest and next nearest neighboring (NNN) lattice sites, while still exhibiting its characteristic symmetry (Aubry–André duality). Previous understanding of the spectral theory of this model was restricted to two dual regions of the parameter space… 

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