Abstract
This dissertation is an examination of the absolutely continuous spectrum for the Anderson model on different types of trees. The text is divided into four chapter: an introduction, two main chapters and conclusions. In Chapter 2 the existence of purely absolutely continuous spectrum is proven for the Anderson model on a Cayley tree, or Bethe lattice, of degree K. The method used, a geometric one, is based on some properties of the hyperbolic distance. It is a simplified generalization of a result for K = 3 given by R. Froese, D. Hasler and W. Spitzer. In Chapter 3 a similar result is proven for a more general tree which has vertices of degrees 2 and 3 alternating in a periodic manner. The lack of symmetry changes the analysis, making it possible to eliminate one of the steps in the proof for the Cayley tree.
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
