September 2010 October 2010 November 2010 Su Mo Tu We Th Fr Sa Su Mo Tu We Th Fr Sa Su Mo Tu We Th Fr Sa 1 2 3 4 1 2 1 2 3 4 5 6 5 6 7 8 9 10 11 3 4 5 6 7 8 9 7 8 9 10 11 12 13 12 13 14 15 16 17 18 10 11 12 13 14 15 16 14 15 16 17 18 19 20 19 20 21 22 23 24 25 17 18 19 20 21 22 23 21 22 23 24 25 26 27 26 27 28 29 30 24 25 26 27 28 29 30 28 29 30 31 |

4:00 pm Wednesday, October 20, 2010 Stulken Geometry-Analysis Seminar: Deterministic Spectral Properties of Anderson-Type Hamiltoniansby
Constanze Liaw (Texas A&M University) in HB 227- An Anderson-type Hamiltonian is a self-adjoint operator on a separable Hilbert space H which is formally given by $A_w = A + V_w$ where $V_w = \sum w_n < . , f_n > f_n$. Here $w=( w_1, w_2, ... )$ is a sequence of independent random variables corresponding to a probability measure on $R^\infty$. Probably the most important Anderson-type Hamiltonian is the discrete random Schroedinger operator. The main result states that under mild cyclicity conditions, the essential parts of two realizations, $A_w$ and $A_v$, are almost surely (with respect to the product measure) unitary equivalent modulo a rank one perturbation. Following ideas developed by A.G.Poltoratski, we will explain how the Krein-Lifshits spectral shift for rank one perturbations plays an important role in the proof.
Submitted by damanik@rice.edu |