5 papers
Continuum Fibonacci Schrödinger Operators in the Strongly Coupled Regime
David Damanik, Mark Embree, Jake Fillman +2
We study Schrödinger operators on the real line whose potentials are generated by the Fibonacci substitution sequence and a rule that replaces symbols by compactly supported poten…
The fibered rotation number
Pedro Duarte, Anton Gorodetski, Victor Kleptsyn
We provide an explicit formula for an increment of the fibered rotation number of a one-parameter family of circle cocycles over any ergodic transformation in terms of invariant me…
Central Limit Theorem for non-stationary random products of $\SL(2, \R)$ matrices
Anton Gorodetski, Victor Kleptsyn, Grigorii Monakov
We prove Central Limit Theorem for non-stationary random products of matrices, generalizing the classical results by Le Page and Tutubalin that were obtained in…
Localization for Random Schrödinger Operators Defined by Block Factors
David Damanik, Anton Gorodetski, Victor Kleptsyn
We consider discrete one-dimensional Schrödinger operators with random potentials obtained via a block code applied to an i.i.d. sequence of random variables. It is shown that, al…
Log Hölder continuity of the rotation number
Anton Gorodetski, Victor Kleptsyn
We consider one-parameter families of smooth circle cocycles over an ergodic transformation in the base, and show that their rotation numbers must be log-Hölder regular with respe…