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It is conjectured that the eigenvalues of random Schrodinger operators at thelocalization transition in dimensions d>=2 behave like the eigenvalues of theGaussian Orthogonal Ensemble (GOE). We show that there are sequences of n by mboxes with 1<<m<<n so that the eigenvalues in low disorder converge to Sine1,the limiting eigenvalue process of the GOE. For the GOE case, this is the firstexample where Wigner's famous prediction is proven rigorously: we exhibit acomplex system whose eigenvalues behave like those of random matrices.

Random Schrodinger operators on long boxes, noise explosion and the GOE