5 papers
The spectral characteristics of the Sturm Hamiltonian with eventually periodic type
Jie Cao, Zhenyu Yu
In this paper we consider the spectral characteristics of the Sturm Hamiltonian with eventually periodic type frequencies under large coupling and establish strict inequalities bet…
The optimal hypercontractive constants for and biased Bernoulli random variables
Jie Cao, Shilei Fan, Yong Han +2
We resolve a folklore problem of determining the optimal hypercontractive constants for the cyclic group for all . More p…
Log-Hausdorff multifractality of the absolutely continuous spectral measure of the almost Mathieu operator
Jie Cao, Xianzhe Li, Baowei Wang +1
This paper focuses on the fractal characteristics of the absolutely continuous spectral measure of the subcritical almost Mathieu operator (AMO) and Diophantine frequency. In parti…
Equilibrium States, Zero Temperature Limits and Entropy Continuity for Almost-Additive Potentials
Jie Cao
This paper is devoted to study the equilibrium states for almost-additive potentials defined over topologically mixing countable Markov shifts (that is a non-compact space) without…
Almost sure dimensional properties for the spectrum and the density of states of Sturmian Hamiltonians
Jie Cao, Yanhui Qu
In this paper, we find a full Lebesgue measure set of frequencies $\check \II\subset [0,1]\setminus \Q$ such that for any $(α,λ)\in \check \II\times [24,\infty)$, the Hausdorff a…