Electronic Journal of Probability

Poisson statistics for 1d Schrödinger operators with random decaying potentials

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
Accepted: 10 August 2017
First available in Project Euclid: 9 September 2017

https://projecteuclid.org/euclid.ejp/1504922532

Digital Object Identifier
doi:10.1214/17-EJP91

Mathematical Reviews number (MathSciNet)
MR3698738

Zentralblatt MATH identifier
06797879

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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