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4 papers
Generic Spectral Results for CMV Matrices with Dynamically Defined Verblunsky Coefficients
Licheng Fang, David Damanik, Shuzheng Guo
We consider CMV matrices with dynamically defined Verblunsky coefficients. These coefficients are obtained by continuous sampling along the orbits of an ergodic transformation. We…
Zero Measure and Singular Continuous Spectra for Quantum Graphs
David Damanik, Licheng Fang, Selim Sukhtaiev
We introduce a dynamically defined class of unbounded, connected, equilateral metric graphs on which the Kirchhoff Laplacian has zero Lebesgue measure spectrum and a nontrivial sin…
Hölder continuity of the Lyapunov exponent for Schrödinger cocycle with quasi-periodic Gevrey potential and weak Liouville frequency
Licheng Fang, Daxiong Piao
For analytic quasi-periodic Schrödinger cocycles, You and Zhang [9] proved that the Lyapunov exponent is Hölder continuous for weak Liouville frequency. In this paper, we prove tha…
Log-Hölder Continuity of the Lyapunov Exponent for Jacobi Operators with Potentials Given by the Skew-Shift
Licheng Fang, Daxiong Piao
In this paper we study one-dimensional Jacobi operators on the lattice with a potential given by the skew shift. We show that the large deviation theorem takes place for Diophantin…