prof. Sadel's seminar at SISSA

[Emanuele Tuillier Illingworth]

SEMINAR ANNOUNCEMENT
--------------------------------------------

Christian Sadel, Institute of Sience and Technology, Klosterneuburg, 
Austria <http://www.ist.ac.at>

Monday the 9th of March at 10.00 am room 136

Title: Absolutely continuous spectrum for the Anderson model on discrete 
graphs

Abstract: The Anderson model is a random Schrödinger operator with 
independent identically distributed potential. Even though Anderson 
localization (pure point spectrum) was the surprise from a physics point 
of view, the appearance of Anderson delocalization, i.e. absolutely 
continuous spectrum for such a random operator, seems mathematically 
harder to be understood.
In high dimensions (d>2) and at low disorder the existence of absolutely 
continuous spectrum is expected. But only on certain graphs such a 
result can be rigorously proved, most of them having an infinite 
dimensional growth in a repeating pattern, such as the Bethe lattice. 
After some introduction I will talk about the development in recent 
years were the list of such graphs has been increased. In particular I 
will also talk about my recent work on antitrees giving the first 
example of a class of models where a transition from localization to 
delocalization happens at the critical 2 dimensional growth rate.