 98318 Jaksic V., Molchanov S.
 On the Surface Spectrum in Dimension Two
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Apr 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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