Electronic Journal of Probability

Poisson statistics for 1d Schrödinger operators with random decaying potentials

Shinichi Kotani and Fumihiko Nakano

Full-text: Open access

Abstract

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

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

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

Permanent link to this document
https://projecteuclid.org/euclid.ejp/1504922532

Digital Object Identifier
doi:10.1214/17-EJP91

Mathematical Reviews number (MathSciNet)
MR3698738

Zentralblatt MATH identifier
06797879

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

Keywords
random Schrödinger operators Poisson statistics Sine beta process

Rights
Creative Commons Attribution 4.0 International License.

Citation

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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References

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