Poisson statistics for 1d Schrödinger operators with random decaying potentials

Shinichi Kotani, Fumihiko Nakano

Research output: Contribution to journalArticle

1 Citation (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 languageEnglish
Article number69
JournalElectronic Journal of Probability
Volume22
DOIs
Publication statusPublished - 2017 Jan 1
Externally publishedYes

Keywords

  • Poisson statistics
  • Random Schrödinger operators
  • Sine beta process

ASJC Scopus subject areas

  • Statistics and Probability
  • Statistics, Probability and Uncertainty

Fingerprint Dive into the research topics of 'Poisson statistics for 1d Schrödinger operators with random decaying potentials'. Together they form a unique fingerprint.

  • Cite this