48 citations · 77 across the 11 of their papers we have counts for
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Schrödinger Operators with Potentials Generated by Hyperbolic Transformations: II. Large Deviations and Anderson Localization
Artur Avila, David Damanik, Zhenghe Zhang
We consider discrete one-dimensional Schrödinger operators whose potentials are generated by Hölder continuous sampling along the orbits of a uniformly hyperbolic transformation. F…
The Schwartzman Group of an Affine Transformation
David Damanik, Íris Emilsdóttir, Jake Fillman
We compute the Schwartzman group associated with an ergodic affine automorphism of a compact connected abelian group given by the composition of an automorphism of the group and a…
Discontinuities of the Integrated Density of States for Laplacians Associated with Penrose and Ammann-Beenker Tilings
David Damanik, Mark Embree, Jake Fillman +1
Aperiodic substitution tilings provide popular models for quasicrystals, materials exhibiting aperiodic order. We study the graph Laplacian associated with four tilings from the mu…
Johnson-Schwartzman Gap Labelling for Ergodic Jacobi Matrices
David Damanik, Jake Fillman, Zhenghe Zhang
We consider two-sided Jacobi matrices whose coefficients are obtained by continuous sampling along the orbits of a homeomorphim of a compact metric space. Given an ergodic probabil…
Cantor Spectrum for CMV Matrices With Almost Periodic Verblunsky Coefficients
Long Li, David Damanik, Qi Zhou
We consider extended CMV matrices with analytic quasi-periodic Verblunsky coefficients with Diophantine frequency vector in the perturbatively small coupling constant regime and pr…
Must the Spectrum of a Random Schrödinger Operator Contain an Interval?
David Damanik, Anton Gorodetski
We consider Schrödinger operators in whose potentials are given by independent (not necessarily identically distributed) random variables. We ask whether it is…