The Weizmann Institute of Science Faculty of Mathematics and Computer Science Mathematical Analysis and Applications Seminar Lecture Hall, Room 1, Ziskind Building on Tuesday, June 21, 2011 11:00 - noon Michael Aizenman Princeton University will speak on Resonant delocalization for Schrodinger operators with random potential on tree graphs Abstract: We resolve an existing question concerning the location of the mobility edge for operators with a hopping term and a random potential on the Bethe lattice. For unbounded potential we find that extended states appear well beyond the spectrum of the operator's hopping term, including in a Lifshitz tail regime of very low density of states. The relevant mechanism is the formation of extended states through disorder enabled resonances, for which the exponential increase of the volume plays an essential role. This mechanism has also the surprising implication that for bounded random potentials at weak disorder there is no mobility edge in the form that was envisioned before. (Joint work with Simone Warzel.) Mathematical Analysis and Applications Seminar Web Page: <http://www.wisdom.weizmann.ac.il/~vered/analsem.html> --------------------------------------------------------- Technion Math Net-2 (TECHMATH2) Editor: Michael Cwikel <techm@math.technion.ac.il> Announcement from: Diana Mandelik <diana.mandelik@weizmann.ac.il>