4:00 pm Wednesday, November 11, 2009
Geometry-Analysis Seminar: Exponential Decay of Green's Function for Discrete Alloy-Type Models on Z
by Martin Tautenhahn (TU Chemnitz) in HB 227
The discrete alloy-type model is given by the random Schrödinger operator Hω = -Δ + Vω on l2(Ζd), where Δ denotes the discrete Laplacian and Vω is a random potential given by the function Vω(x) = ∑k∈Zdωku( x - k). Here ω = {ωk}k∈Zd is a sequence of independent identically distributed random variables and u : Ζd → R is assumed to have compact support. We also assume that the distribution of ω0 has a density p ∈ L∞(R). Note that the single-site potential u may change its sign. In this talk we show exponential decay of Green's function in the one dimensional situation via the fractional moment method. We also discuss localization properties and partial results in higher dimension. Host Department: Rice University-Mathematics
Submitted by mathweb@rice.edu |
