Electronic Journal of Probability

Poisson statistics for 1d Schrödinger operators with random decaying potentials

Shinichi Kotani and Fumihiko Nakano

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

Article information

Electron. J. Probab., Volume 22 (2017), paper no. 69, 31 pp.

Received: 28 June 2016
Accepted: 10 August 2017
First available in Project Euclid: 9 September 2017

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Zentralblatt MATH identifier

Primary: 60F05: Central limit and other weak theorems 60H25: Random operators and equations [See also 47B80]

random Schrödinger operators Poisson statistics Sine beta process

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Kotani, Shinichi; Nakano, Fumihiko. Poisson statistics for 1d Schrödinger operators with random decaying potentials. Electron. J. Probab. 22 (2017), paper no. 69, 31 pp. doi:10.1214/17-EJP91. https://projecteuclid.org/euclid.ejp/1504922532

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