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4:00 pm Wednesday, November 11, 2009 Geometry-Analysis Seminar: Exponential Decay of Green's Function for Discrete Alloy-Type Models on Zby Martin Tautenhahn (TU Chemnitz) in HB 227- The discrete alloy-type model is given by the random Schrödinger operator
H_{ω} = -Δ + V_{ω} on l^{2}(Ζ^{d}), where Δ denotes the discrete Laplacian and V_{ω} is a random potential given by the function V_{ω}(x) = ∑_{k∈Zd}ω(_{k}u x - k). Here ω = {ω_{k}}_{k∈Zd} is a sequence of independent identically distributed random variables and u : Ζ → ^{d}R is assumed to have compact support. We also assume that the distribution of ω_{0} 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.Submitted by mathweb@rice.edu |