98-619 Jaksic V., Molchanov S.

On the Surface Spectrum in Dimension Two - revised version. (667K, postscript) Sep 28, 98

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Abstract. We study spectral properties of the discrete Laplacian $H_\omega$ on the half space ${\bf Z}_+^2 = {\bf Z}\times {\bf Z}_+$ with a random boundary condition $\psi(n,-1) = V_\omega(n)\psi(n,0)$. Here, $V_\omega(n)$ are independent and identically distributed random variables on a probability space $(\Omega, {\cal F}, P)$. We show that outside the interval $[-4,4]$ (the spectrum of the Dirichlet Laplacian) the spectrum of $H_\omega$ is $P$-a.s. dense pure point.

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