矩阵值Anderson模型IDS的Hölder连续性
Hölder continuity of the IDS for matrix-valued Anderson models
摘要：
研究了一类作用在$L^{2}(\R^{d})\otimes \C^{N}$上的连续矩阵值Anderson模型.我们证明了对任何$d\geq 1$和$N\geq 1$都存在积分态密度。然后对$d=1$和任意的$N$，在与模型相关联的转移矩阵所生成的群$G_{μ_{E}}$的某些假设下，证明了积分态密度的Hölder连续性.这个规律性的结果是基于与我们的模型相关联的Lyapounov指数的类似规律性，以及一个新的无偏公式，该公式将正Lyapounov指数的总和与积分态密度联系起来。在最后一节中，我们给出了一个矩阵值Anderson模型的例子，我们已经证明了，在以前的文章中，对组$G_{μ_{E}}$的假设得到了验证。因此，这里开发的一般结果可以应用到这个模型。
英文摘要：
We study a class of continuous matrix-valued Anderson models acting on $L^{2}(\R^{d})\otimes \C^{N}$. We prove the existence of their Integrated Density of States for any $d\geq 1$ and $N\geq 1$. Then for $d=1$ and for arbitrary $N$, we prove the Hölder continuity of the Integrated Density of States under some assumption on the group $G_{μ_{E}}$ generated by the transfer matrices associated to our models. This regularity result is based upon the analoguous regularity of the Lyapounov exponents associated to our model, and a new Thouless formula which relates the sum of the positive Lyapounov exponents to the Integrated Density of States. In the final section, we present an example of matrix-valued Anderson model for which we have already proved, in a previous article, that the assumption on the group $G_{μ_{E}}$ is verified. Therefore the general results developed here can be applied to this model.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
