8 citations · 24 across the 13 of their papers we have counts for
14 papers
Polynomial Spectral Gap Estimates for Finitely Differentiable Quasi-Periodic Schrödinger Operators
Ao Cai, Yang Gao, Jiawei He
We prove polynomial upper bounds on spectral gaps of quasi-periodic Schrödinger operators with small potentials and Diophantine frequencies. For sufficiently large , the…
Arithmetic -Polynomial Dynamical Localization for Power-Law Quasi-Periodic Long-Range Operators on
Ao Cai, Huihui Lv, Yuan Shan +1
We establish a criterion of arithmetic -polynomial spectral localization and -polynomial dynamical localization in expectation for quasi-periodic long-range operators on $\el…
Abstract Continuity Theorem for the Lyapunov Exponents of linear cocycles
Ao Cai, Xiaojuan Deng
We prove the Hölder continuity of Lyapunov exponents for general linear cocycles when the base measures vary in Wasserstein distance, under the assumption of uniform large deviatio…
Quantitative Reducibility of Quasi-Periodic Cocycles
Ao Cai, Huihui Lv, Zhiguo Wang
This paper establishes an extreme reducibility theorem of quasi-periodic cocycles in the local perturbative region, revealing both the essence of Eliasson…
Randomness versus quasi-periodicity
Ao Cai
This paper serves as an extended road map for our long-term project "Mixed Random-quasiperiodic Cocycles" [arXiv:2201.04745, arXiv:2109.09544, arXiv:2210.16908, 6, 7] with Pedro Du…
Hölder continuity of the Lyapunov exponent for Markov cocycles via Furstenberg's Formula
Ao Cai, Marcelo Durães, Silvius Klein +1
This paper is concerned with the study of linear cocycles over uniformly ergodic Markov shifts on a compact space of symbols. We establish the joint Hölder continuity of the maxima…
Statistical properties for mixing Markov chains with applications to dynamical systems
Ao Cai, Pedro Duarte, Silvius Klein
We establish an abstract, effective, exponential large deviations type estimate for Markov systems satisfying a weaker form of mixing. We employ this result to derive such estimate…
A dynamical Thouless formula
Jamerson Bezerra, Ao Cai, Pedro Duarte +2
In this paper we establish an abstract, dynamical Thouless-type formula for affine families of cocycles. This result extends the classical formula rela…
Furstenberg Theory of Mixed Random-Quasiperiodic Cocycles
Ao Cai, Pedro Duarte, Silvius Klein
We derive a criterion for the positivity of the maximal Lyapunov exponent of generic mixed random-quasiperiodic linear cocycles, a model introduced in a previous work. This result…
Mixed Random-Quasiperiodic Cocycles
Ao Cai, Pedro Duarte, Silvius Klein
We introduce the concept of mixed random-quasiperiodic linear cocycles. We characterize the ergodicity of the base dynamics and establish a large deviations type estimate for certa…
The absolutely continuous spectrum of finitely differentiable quasi-periodic Schrödinger operators
Ao Cai
We prove that the quasi-periodic Schrödinger operator with a finitely differentiable potential has purely absolutely continuous spectrum for all phases if the frequency is Diophant…
Polynomial decay of the gap length for C^k quasi-periodic Schrodinger operators and spectral application
Ao Cai, Xueyin Wang
For the quasi-periodic Schrödinger operators in the local perturbative regime where the frequency is Diophantine and the potential is sufficiently small depending on the Diop…
Reducibility of finitely differentiable quasi-periodic cocycles and its spectral applications
Ao Cai, Lingrui Ge
In this paper, we prove the generic version of Cantor spectrum for quasi-periodic Schrödinger operators with finitely smooth and small potentials, and we also show pure point spect…
Sharp Holder continuity of the Lyapunov exponent of finitely differentiable quasi-periodic cocycles
Ao Cai, Claire Chavaudret, Jiangong You +1
We show that if the base frequency is Diophantine, then the Lyapunov exponent of a quasi-periodic cocycle is -Hölder continuous in the almost reduci…