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arxiv: 1605.02416 · v2 · pith:MFJ5S7K3new · submitted 2016-05-09 · 🧮 math-ph · math.MP· math.PR

Poisson statistics for 1d Schr\"odinger operators with random decaying potentials

classification 🧮 math-ph math.MPmath.PR
keywords decayingodingeroperatorspointpoissonpotentialsprocessrandom
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We consider the 1d Schr\"odinger 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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