Wigner和确定性对角矩阵中自伴随多项式经验谱分布的Stieltjes变换波动

IF 1.6 2区数学 Q1 MATHEMATICS

Journal of Functional Analysis Pub Date : 2025-05-30 DOI:10.1016/j.jfa.2025.111083

Serban Belinschi , Mireille Capitaine , Sandrine Dallaporta , Maxime Fevrier

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引用次数: 0

摘要

研究了Wigner矩阵和确定对角矩阵中任意自伴非交换多项式的经验谱分布的Stieltjes变换均值附近的波动。得到了协方差用算子值隶属函数表示的有中心的复高斯过程在分布上的收敛性。

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Fluctuations of the Stieltjes transform of the empirical spectral distribution of selfadjoint polynomials in Wigner and deterministic diagonal matrices

We investigate the fluctuations around the mean of the Stieltjes transform of the empirical spectral distribution of any selfadjoint noncommutative polynomial in a Wigner matrix and a deterministic diagonal matrix. We obtain the convergence in distribution to a centered complex Gaussian process whose covariance is expressed in terms of operator-valued subordination functions.

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来源期刊

Journal of Functional Analysis 数学-数学

CiteScore

3.20

自引率

5.90%

发文量

271

审稿时长

7.5 months

期刊介绍： The Journal of Functional Analysis presents original research papers in all scientific disciplines in which modern functional analysis plays a basic role. Articles by scientists in a variety of interdisciplinary areas are published. Research Areas Include: • Significant applications of functional analysis, including those to other areas of mathematics • New developments in functional analysis • Contributions to important problems in and challenges to functional analysis