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Poisson statistics for 1d Schrödinger operators with random decaying potentials
Shinichi Kotani, Fumihiko Nakano · 2016-05-09 · via math.PR updates on arXiv.org

We consider the 1d Schrödinger operators with random decaying potentials where the spectrum is pure point(sub-critical case). We show that the point process composed of the rescaled eivenvalues, together with those zero points of the corresponding eigenfunctions, converges to the Poisson process.

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