ON TORAL EIGENFUNCTIONS AND THE RANDOM WAVE MODEL

被引：24

作者：

Bourgain, Jean ^{[1
]}

机构：

[1] Inst Adv Study, Sch Math, Princeton, NJ 08540 USA

来源：

ISRAEL JOURNAL OF MATHEMATICS | 2014年 / 201卷 / 02期

关键词：

POINTS;

D O I：

10.1007/s11856-014-1037-z

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

The purpose of this Note is to provide a deterministic implementation of the random wave model for the number of nodal domains in the context of the two-dimensional torus. The approach is based on recent work due to Nazarov and Sodin and arithmetical properties of lattice points on circles.

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收藏

页码：611 / 630

页数：20

相关论文

共 14 条

[1]

[Anonymous], LECT RANDOM NODAL PO

[2] Statistics of nodal lines and points in chaotic quantum billiards: perimeter corrections, fluctuations, curvature [J].

Berry, MV .

JOURNAL OF PHYSICS A-MATHEMATICAL AND GENERAL, 2002, 35 (13) :3025-3038

[3] Random wavefunctions and percolation [J].

Bogomolny, E. ;

Schmit, C. .

JOURNAL OF PHYSICS A-MATHEMATICAL AND THEORETICAL, 2007, 40 (47) :14033-14043

[4] Percolation model or nodal domains of chaotic wave functions [J].

Bogomolny, E ;

Schmit, C .

PHYSICAL REVIEW LETTERS, 2002, 88 (11) :4

[5]

Bombieri E., INT MATH RE IN PRESS

[6]

Bourgain J., INT MATH RE IN PRESS

[7] On the angular distribution of Gaussian integers with fixed norm [J].

Erdos, P ;

Hall, RR .

DISCRETE MATHEMATICS, 1999, 200 (1-3) :87-94

[8] Linear equations in variables which lie in a multiplicative group [J].

Evertse, JH ;

Schlickewei, HP ;

Schmidt, WM .

ANNALS OF MATHEMATICS, 2002, 155 (03) :807-836

[9] Lattice points on circles and discrete velocity models for the Boltzmann equation [J].

Fainsilber, L ;

Kurlberg, P ;

Wennberg, B .

SIAM JOURNAL ON MATHEMATICAL ANALYSIS, 2006, 37 (06) :1903-1922

[10] Nodal Domains of Maass Forms I [J].

Ghosh, Amit ;

Reznikov, Andre ;

Sarnak, Peter .

GEOMETRIC AND FUNCTIONAL ANALYSIS, 2013, 23 (05) :1515-1568