Poisson statistics for 1d Schrodinger operators with random decaying potentials

被引：9

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.

引用

页数：31

共 14 条

[1] From Sine kernel to Poisson statistics [J].

Allez, Romain ;

Dumaz, Laure .

ELECTRONIC JOURNAL OF PROBABILITY, 2014, 19

[2] Tracy-Widom at High Temperature [J].

Allez, Romain ;

Dumaz, Laure .

JOURNAL OF STATISTICAL PHYSICS, 2014, 156 (06) :1146-1183

[3] BULK UNIVERSALITY AND CLOCK SPACING OF ZEROS FOR ERGODIC JACOBI MATRICES WITH ABSOLUTELY CONTINUOUS SPECTRUM [J].

Avila, Artur ;

Last, Yoram ;

Simon, Barry .

ANALYSIS & PDE, 2010, 3 (01) :81-108

[4] EIGENVALUE STATISTICS FOR CMV MATRICES: FROM POISSON TO CLOCK VIA RANDOM MATRIX ENSEMBLES [J].

Kilip, Rowan ;

Stoiciu, Mihai .

DUKE MATHEMATICAL JOURNAL, 2009, 146 (03) :361-399

[5] Eigenfunction statistics in the localized Anderson model [J].

Killip, Rowan ;

Nakano, Fumihiko .

ANNALES HENRI POINCARE, 2007, 8 (01) :27-36

[6] Modified Prufer and EFGP transforms and the spectral analysis of one-dimensional Schrodinger operators [J].

Kiselev, A ;

Last, Y ;

Simon, B .

COMMUNICATIONS IN MATHEMATICAL PHYSICS, 1998, 194 (01) :1-45

[7] ONE-DIMENSIONAL SCHRODINGER-OPERATORS WITH RANDOM DECAYING POTENTIALS [J].

KOTANI, S ;

USHIROYA, N .

COMMUNICATIONS IN MATHEMATICAL PHYSICS, 1988, 115 (02) :247-266

[8]

Kotani S., 2014, Interdiscip. Math. Sci, V17, P343, DOI [10.1142/9789814596534_0018, DOI 10.1142/9789814596534_0018]

[9] The Scaling Limit of the Critical One-Dimensional Random Schrodinger Operator [J].

Kritchevski, Eugene ;

Valko, Benedek ;

Virag, Balint .

COMMUNICATIONS IN MATHEMATICAL PHYSICS, 2012, 314 (03) :775-806

[10]

Nakano F., 2015, RIMS KOKYUROKU, V1970, P83

← 1 2 →