The integrated density of states of the 1D discrete Anderson–Bernoulli model at rational energies

@article{SanchezMendoza2022TheID,
  title={The integrated density of states of the 1D discrete Anderson–Bernoulli model at rational energies},
  author={Daniel S'anchez-Mendoza},
  journal={Journal of Mathematical Physics},
  year={2022}
}
Much is known about the Anderson-Bernoulli model on Z. In 1894, Delyon and Souillard gave an elementary proof of the continuity of the integrated density of states (IDS). Spectral localization on the whole spectrum at any disorder was proven in 1987 by Carmona, Klein and Martinelli using Furstenberg’s theorem and multi-scale analysis. Later that same year Martinelli and Micheli gave a lower bound, uniform over the spectrum, on the asymptotic of the Lyapunov exponent as the disorder parameter… 

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References

SHOWING 1-6 OF 6 REFERENCES
Sharp bounds for the integrated density of states of a strongly disordered 1D Anderson–Bernoulli model
In this article we give upper and lower bounds for the integrated density of states (IDS) of the 1D discrete Anderson-Bernoulli model when the disorder is strong enough to separate the two spectral
Anderson localization for Bernoulli and other singular potentials
We prove exponential localization in the Anderson model under very weak assumptions on the potential distribution. In one dimension we allow any measure which is not concentrated on a single point
On the large-coupling-constant behavior of the Liapunov exponent in a binary alloy
We consider the usual one-dimensional tight-binding Anderson model with the random potential taking only two values, 0 andλ, with probabilityp and 1−p, 0<p<1. We show that the Liapunov exponentγλ(E),
Lifshitz tails for the 1D Bernoulli-Anderson model
By using the adequate modified Pr\"ufer variables, precise upper and lower bounds on the density of states in the (internal) Lifshitz tails are proven for a 1D Anderson model with bounded potential.
Chebyshev Polynomials
This paper is a short exposition of several magnificent properties of the Chebyshev polynomials. The author illustrates how the Chebyshev polynomials arise as solutions to two optimization problems.
Remark on the continuity of the density of states of ergodic finite difference operators
We give an elementary proof that for a large class ofd-dimensional finite difference operators including tight-binding models for electron propagation and models for harmonic phonons with random