- 02-471 David Damanik, Robert Sims, G\"unter Stolz
- Localization for discrete one dimensional random word models
Nov 20, 02
(auto. generated ps),
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Abstract. We consider discrete one-dimensional Schr\"odinger operators whose
potentials are obtained by randomly concatenating words from an
underlying word space according to some probability measure. 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 Furstenberg's theorem to verify the necessary
input to perform a multiscale analysis.