BULK UNIVERSALITY AND CLOCK SPACING OF ZEROS FOR ERGODIC JACOBI MATRICES WITH ABSOLUTELY CONTINUOUS SPECTRUM

被引：29

作者：

Avila, Artur ^{[1
,2
]}

Last, Yoram ^{[3
]}

Simon, Barry ^{[4
]}

机构：

[1] Univ Paris 06, CNRS, Lab Probabil & Modeles Aleatoires, UMR 7599, F-75252 Paris 05, France

[2] Inst Nacl Matemat Pura & Aplicada, BR-22460320 Rio De Janeiro, Brazil

[3] Hebrew Univ Jerusalem, Inst Math, IL-91904 Jerusalem, Israel

[4] CALTECH, Dept Math, Pasadena, CA 91125 USA

来源：

ANALYSIS & PDE | 2010年 / 3卷 / 01期

基金：

以色列科学基金会; 美国国家科学基金会;

关键词：

orthogonal polynomials; clock behavior; almost Mathieu equation; LATTICE SCHRODINGER-OPERATORS; ORTHOGONAL POLYNOMIALS; FINE-STRUCTURE; LIMITS; KERNELS; BOUNDS;

D O I：

10.2140/apde.2010.3.81

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

By combining ideas of Lubinsky with some soft analysis, we prove that universality and clock behavior of zeros for orthogonal polynomials on the real line in the absolutely continuous spectral region is implied by convergence of 1/nK(n) (x, x) for the diagonal CD kernel and boundedness of the analog associated to second kind polynomials. We then show that these hypotheses are always valid for ergodic Jacobi matrices with absolutely continuous spectrum and prove that the limit of 1/nK(n)(x, x) is rho(infinity)(x)/w(x), where rho(infinity) is the density of zeros and w is the absolutely continuous weight of the spectral measure.

引用

页码：81 / 108

页数：28