Perturbed Toeplitz operators and radial determinantal processes

被引：0
|
作者：
Ehrhardt, Torsten [1 ]
Rider, Brian [2 ]
机构：
[1] Univ Calif Santa Cruz, Dept Math, Santa Cruz, CA 95064 USA
[2] Univ Colorado, Dept Math, Boulder, CO 80309 USA
来源：
ANNALES DE L INSTITUT HENRI POINCARE-PROBABILITES ET STATISTIQUES | 2013年 / 49卷 / 04期
关键词：
Random matrices; Determinantal processes; Toeplitz operators; Szego-Widom limit theorem; RANDOM MATRICES; LIMIT;
D O I：
10.1214/12-AIHP501
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 study a class of rotation invariant determinantal ensembles in the complex plane; examples include the eigenvalues of Gaussian random matrices and the roots of certain families of random polynomials. The main result is a criterion for a central limit theorem to hold for angular statistics of the points. The proof exploits an exact formula relating the generating function of such statistics to the determinant of a perturbed Toeplitz matrix.
引用
收藏
页码：934 / 960
页数：27
相关论文
共 50 条
  • [21] Toeplitz operators on the Fock space: Radial component effects
    Grudsky, SM
    Vasilevski, NL
    INTEGRAL EQUATIONS AND OPERATOR THEORY, 2002, 44 (01) : 10 - 37
  • [22] Numerical Ranges of Radial Toeplitz Operators on Bergman Space
    Wang, Kuo Zhong
    Wu, Pei Yuan
    INTEGRAL EQUATIONS AND OPERATOR THEORY, 2009, 65 (04) : 581 - 591
  • [23] Kernels of perturbed Toeplitz operators in vector-valued Hardy spaces
    Chattopadhyay, Arup
    Das, Soma
    Pradhan, Chandan
    ADVANCES IN OPERATOR THEORY, 2021, 6 (03)
  • [24] A probabilistic Weyl-law for perturbed Berezin-Toeplitz operators
    Oltman, Izak
    JOURNAL OF SPECTRAL THEORY, 2023, 13 (02) : 727 - 754
  • [25] Spectral properties of harmonic Toeplitz operators and applications to the perturbed Krein Laplacian
    Bruneau, Vincent
    Raikov, Georgi
    ASYMPTOTIC ANALYSIS, 2018, 109 (1-2) : 53 - 74
  • [26] Kernels of perturbed Toeplitz operators in vector-valued Hardy spaces
    Arup Chattopadhyay
    Soma Das
    Chandan Pradhan
    Advances in Operator Theory, 2021, 6
  • [27] Toeplitz Operators with Radial Symbols on General Analytic Function Spaces
    Alexey Karapetyants
    Jari Taskinen
    Complex Analysis and Operator Theory, 2022, 16
  • [28] ON AN ALGEBRA CONNECTED WITH TOEPLITZ-OPERATORS IN RADIAL TUBE DOMAINS
    VASILEVSKII, NL
    MATHEMATICS OF THE USSR-IZVESTIYA, 1987, 51 (01): : 71 - 88
  • [29] Toeplitz Operators on the Weighted Pluriharmonic Bergman Space with Radial Symbols
    Sun, Zhi Ling
    Lu, Yu Feng
    ABSTRACT AND APPLIED ANALYSIS, 2011,
  • [30] Radial Toeplitz operators on the weighted Bergman spaces of Cartan domains
    Dawson, Matthew
    Quiroga-Barranco, Raul
    REPRESENTATION THEORY AND HARMONIC ANALYSIS ON SYMMETRIC SPACES, 2018, 714 : 97 - 114
12345