# Level statistics of one-dimensional schrödinger operators with random decaying potential

Shinichi Kotani, Fumihiko Nakano

6 被引用数 (Scopus)

## 抄録

We study the level statistics of one-dimensional Schrödinger operator with random potential decaying like x-a at infinity. We consider the point process L consisting of the rescaled eigenvalues and show that: (i) (ac spectrum case) for formula, L converges to a clock process, and the fluctuation of the eigenvalue spacing converges to Gaussian. (ii) (critical case) for formula, L converges to the limit of the circular ß-ensemble.

本文言語 English Festschrift Masatoshi Fukushima In Honor Of Masatoshi Fukushima’s Sanju World Scientific Publishing Co. 343-373 31 9789814596534 https://doi.org/10.1142/9789814596534_0018 Published - 2014 11 27 はい

## ASJC Scopus subject areas

• 数学 (全般)
• 物理学および天文学（全般）

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