98-317 Jaksic V., Molchanov S.
Localization for One Dimensional Long Range Random Hamiltonians - revised and extended version. (740K, postscript) Apr 28, 98
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Abstract. We study spectral properties of random Schr\"odinger operators $h_\omega = h_0 + v_\omega(n)$ on $l^2({\bf Z})$ whose free part $h_0$ is long range. We prove that the spectrum of $h_\omega$ is pure point for typical $\omega$ whenever the off-diagonal terms of $h_0$ decay as $\vert i -j\vert^{-\gamma}$ for some $\gamma >8$.

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