论文标题
$ \ ell^2（\ z^d）$的准周期远程运营商的综合状态密度的Hölder规律性
Hölder regularity of the integrated density of states for quasi-periodic long-range operators on $\ell^2(\Z^d)$
论文作者
论文摘要
我们证明了$ \ ell^2（\ z^d）$具有较大的三角多项式电势和双苯胺频率的$ \ ell^2（\ z^d）$上一类的状态密度的Hölder连续性。此外，我们从电势水平集的基数方面给出了Hölder指数，该水平集得到了扰动状态，该结果由Goldstein和Schlag \ cite \ cite {gs2}获得的结果。我们的方法是aubry二元性，一般性的公式和分析性准周期$ gl（m，\ c）$ cocycles的lyapunov指数的规律性的结合，这是通过定量可降低性方法证明的。
We prove the Hölder continuity of the integrated density of states for a class of quasi-periodic long-range operators on $\ell^2(\Z^d)$ with large trigonometric polynomial potentials and Diophantine frequencies. Moreover, we give the Hölder exponent in terms of the cardinality of the level sets of the potentials, which improves, in the perturbative regime, the result obtained by Goldstein and Schlag \cite{gs2}. Our approach is a combination of Aubry duality, generalized Thouless formula and the regularity of the Lyapunov exponents of analytic quasi-periodic $GL(m,\C)$ cocycles which is proved by quantitative almost reducibility method.
