Hölder continuity of the IDS for matrixvalued Anderson models
Abstract
We study a class of continuous matrixvalued 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 $G_{\mu_{E}}$ 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 matrixvalued Anderson model for which we have already proved, in a previous article, that the assumption on the group $G_{\mu_{E}}$ is verified. Therefore the general results developed here can be applied to this model.
 Publication:

arXiv eprints
 Pub Date:
 November 2007
 arXiv:
 arXiv:0711.3889
 Bibcode:
 2007arXiv0711.3889H
 Keywords:

 Mathematical Physics
 EPrint:
 Rev. Math. Phys. 20(7). 873900 (2008)