Localization for discrete one-dimensional random word models

We consider Schrödinger operators in ℓ2(Z) whose potentials are obtained by randomly concatenating words from an underlying set W according to some probability measure ν on W. Our assumptions allow us to consider models with local correlations, such as the random dimer model or, more generally, random polymer models. We prove spectral localization and, away from a finite set of exceptional energies, dynamical localization for such models. These results are obtained by employing scattering theoretic methods together with Furstenbergʹs theorem to verify the necessary input to perform a multiscale analysis.