Poisson statistics for 1d Schrödinger operators with random decaying potentials

Shinichi Kotani; Fumihiko Nakano

doi:10.1214/17-EJP91

Poisson statistics for 1d Schrödinger operators with random decaying potentials

Shinichi Kotani, Fumihiko Nakano

SCI - Mathematics

Osaka University

Research output: Contribution to journal › Article › peer-review

5 Citations (Scopus)

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.

Original language	English
Article number	69
Journal	Electronic Journal of Probability
Volume	22
DOIs	https://doi.org/10.1214/17-EJP91
Publication status	Published - 2017

Keywords

Poisson statistics
Random Schrödinger operators
Sine beta process

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10.1214/17-EJP91

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title = "Poisson statistics for 1d Schr{\"o}dinger operators with random decaying potentials",

abstract = "We consider the 1d Schr{\"o}dinger 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.",

keywords = "Poisson statistics, Random Schr{\"o}dinger operators, Sine beta process",

author = "Shinichi Kotani and Fumihiko Nakano",

year = "2017",

doi = "10.1214/17-EJP91",

language = "English",

volume = "22",

journal = "Electronic Journal of Probability",

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AU - Kotani, Shinichi

AU - Nakano, Fumihiko

PY - 2017

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AB - 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.

KW - Poisson statistics

KW - Random Schrödinger operators

KW - Sine beta process

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VL - 22

JO - Electronic Journal of Probability

JF - Electronic Journal of Probability

M1 - 69

ER -

Poisson statistics for 1d Schrödinger operators with random decaying potentials

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