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On random Schrödinger operators on $\mathbb Z^2$

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  • This paper is concerned with random lattice operators on $\mathbb Z^2$ of theform $H_\omega = \Delta + V_\omega$ where $\Delta$ is the lattice Laplacian and $V_\omega$ a random potential$V_\omega(n) = \omega_nv_n, \{\omega_n\}$ independent Bernoulli or Gaussian variables and $\{v_n\}$ satisfyingthe condition sup$_n |v_n| |n|^\rho < \infty$ for some $\rho>\frac{1}{2}$. In this setting and restrictingthe spectrum away from the edges and 0, existence and completeness of the waveoperators is shown. This leads to statements on the a.c. spectrum of $H_\omega$. It shouldbe pointed out that, although we do consider here only a specific (and classical)model, the core of our analysis does apply in greater generality.
    Mathematics Subject Classification: 4730, 47A40, 34F05.


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