## Diff. Geom, Math. Phys., PDE Seminar: Christian Sadel

- Date: 10/16/2012

*UBC*

University of British Columbia

Absolutely continuous spectrum for random SchrÃ¶dinger operators on tree-strips of finite cone-type.

One of the biggest challenges in the field of random SchrÃ¶dinger operators is to prove the existence of absolutely continuous spectrum for the Anderson model for small disorder in dimensions greater equal to 3. So far, the existence of absolutely continuous spectrum is only known for models on infinite-dimensional tree structures. The first proof, done by Abel Klein for a regular tree, dates back to 1994.

Recent developments considered trees of finite cone type and cross products of trees with finite graphs, so called tree-strips. I will present a proof for the existence of absolutely continuous spectrum for models on tree-strips of finite cone type. The proof uses a version of the Implicit Function Theorem in Banach spaces which are constructed by a supersymmetric formalism using Grassmann variables.

Location: ESB 2012