Spectral statistic for decaying random potentials

We consider Anderson model $H^ω=-Δ+V^ω$ on $\ell^2(\mathbb{Z}^d)$ with decaying random potential. We study the point process $ξ^ω_{L,λ}$ associated with eigenvalues of $H^ω_{Λ_L}$, the retriction of $H^ω$ to the finite cube $Λ_L$. Our result is that the weak limit points of $\{ξ^ω_{L,λ}\}$ are poisson point processes as $L\to\infty$.

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