Localization of Surface Spectra |
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Authors: | Vojkan Jakšić Stanislav Molchanov |
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Affiliation: | (1) Department of Mathematics and Statistics, University of Ottawa, 585 King Edward Avenue, Ottawa, ON, K1N 6N5, Canada, CA;(2) Department of Mathematics, University of North Carolina, Charlotte, NC 28223, USA, US |
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Abstract: | We study spectral properties of the discrete Laplacian H on the half-space with random boundary condition ; the V(n) are independent random variables on a probability space and λ is the coupling constant. It is known that if the V(n) have densities, then on the interval [-2(d+1), 2(d+1)] (=σ(H 0), the spectrum of the Dirichlet Laplacian) the spectrum of H is P-a.s. absolutely continuous for all λ [JL1]. Here we show that if the random potential P satisfies the assumption of Aizenman–Molchanov [AM], then there are constants λ d and Λ d such that for |λ| d and |λ|> Λ d the spectrum of H outside σ(H 0) is P-a.s. pure point with exponentially decaying eigenfunctions. Received: 3 December 1998 / Accepted: 27 May 1999 |
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