10 citations · 11 across the 5 of their papers we have counts for
5 papers
Equivalent Conditions for Domination of -sequences
Chang Sun, Zhenghe Zhang
It is well known that a -sequence is uniformly hyperbolic if and only it satisfies a uniform exponential growth condition. Similarly, for $\mathrm{GL}(2,…
On the Correspondence Between Domination and the Spectrum of Jacobi Operators
Kateryna Alkorn, Zhenghe Zhang
In this paper, we first develop a notion of dominated splitting for -sequences and show it is a stable property under -perturbation. Then…
Schrödinger Operators With Potentials Generated by Hyperbolic Transformations: I. Positivity of the Lyapunov Exponent
Artur Avila, David Damanik, Zhenghe Zhang
We consider discrete one-dimensional Schrödinger operators whose potentials are generated by sampling along the orbits of a general hyperbolic transformation. Specifically, we show…
Positive Lyapunov Exponents and a Large Deviation Theorem for Continuum Anderson Models, Briefly
Valmir Bucaj, David Damanik, Jake Fillman +4
In this short note, we prove positivity of the Lyapunov exponent for 1D continuum Anderson models by leveraging some classical tools from inverse spectral theory. The argument is m…
Localization for the one-dimensional Anderson model via positivity and large deviations for the Lyapunov exponent
Valmir Bucaj, David Damanik, Jake Fillman +4
We provide a complete and self-contained proof of spectral and dynamical localization for the one-dimensional Anderson model, starting from the positivity of the Lyapunov exponent…