Poisson statistics for 1d Schrodinger operators with random decaying potentials

被引：8
|
作者：
Kotani, Shinichi [1 ]
Nakano, Fumihiko [2 ]
机构：
[1] Osaka Univ, Dept Math, Machikaneyamachou 1-1, Toyonaka, Osaka 5600043, Japan
[2] Gakushuin Univ, Dept Math, Toshima Ku, 1-5-1 Mejiro, Tokyo 1718588, Japan
来源：
ELECTRONIC JOURNAL OF PROBABILITY | 2017年 / 22卷
基金：
英国工程与自然科学研究理事会;
关键词：
random Schrodinger operators; Poisson statistics; Sine beta process;
D O I：
10.1214/17-EJP91
中图分类号：
O21 [概率论与数理统计]; C8 [统计学];
学科分类号：
020208 ; 070103 ; 0714 ;
摘要：
We consider the 1d Schrodinger 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.
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页数：31
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