4 citations · 10 across the 7 of their papers we have counts for
7 papers
Discontinuity of Lyapunov exponent in spaces of quasiperiodic cocycles: Smoothness vs Arithmetic
Jinhao Liang, Kai Tao, Jiangong You
We construct examples of discontinuity of Lyapunov exponent in the spaces of quasiperiodic -cocycles for fixed irrational frequencies. Especially, we prov…
Homogeneous Spectrum of Quasi-periodic Gevrey Schrödinger Operators with Diophantine Frequency
Yan Yang, Kai Tao
We consider the quasi-periodic Schrödinger operator with the non-degenerate Gevrey potential for the Diophantine frequency. We prove that if the coupling number of the potential is…
Large Deviation theorems for Dirichlet determinants of analytic quasi-periodic Jacobi operators with Brjuno-Rüssmann frequency
Wenmeng Geng, Kai Tao
In this paper, we first study the strong Birkhoff Ergodic Theorem for subharmonic functions with the Brjuno-Rüssmann shift on the Torus. Then, we apply it to prove the large deviat…
Strong Birkhoff Ergodic Theorem for subharmonic functions with irrational shift and its application to analytic quasi-periodic cocycles
Kai Tao
In this paper, we first prove the strong Birkhoff Ergodic Theorem for subharmonic functions with the irrational shift on the Torus. Then, it is applied to the analytic quasi-period…
Non-perturbative positive Lyapunov exponent of Schrödinger equations and its applications to skew-shift
Kai Tao
We first study the discrete Schrödinger equations with analytic potentials given by a class of transformations. It is shown that if the coupling number is large, then its logarithm…
Hölder continuity of the integrated density of states for quasi-periodic Jacobi operators
Kai Tao, Mircea Voda
We show Hölder continuity for the integrated density of states of a quasi-periodic Jacobi operator with analytic coefficients, in the regime of positive Lyapunov exponent and with…
Hölder continuity of Lyapunov exponent for quasi-periodic Jacobi operators
Kai Tao
We consider the quasi-periodic Jacobi operator in where $a(…