Hölder continuity of the IDS for matrix-valued Anderson models
| dc.creator | Hakim, Boumaza | |
| dc.date | 2007-11-25 | |
| dc.date | 2007-11-30 | |
| dc.date.accessioned | 2026-07-07T10:03:34Z | |
| dc.date.available | 2026-07-07T10:03:34Z | |
| dc.description | 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. | |
| dc.identifier | https://arxiv.org/abs/0711.3889 | |
| dc.identifier | http://arxiv.org/abs/0711.3889 | |
| dc.identifier | Rev. Math. Phys. 20(7). 873-900 (2008) | |
| dc.identifier | doi:10.1142/S0129055X08003456 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/169336 | |
| dc.subject | Mathematical Physics | |
| dc.title | Hölder continuity of the IDS for matrix-valued Anderson models | |
| dc.type | text |