Wigner矩阵特征多项式的最优刚度和最大值

IF 2.4 1区数学 Q1 MATHEMATICS

Geometric and Functional Analysis Pub Date : 2025-02-05 DOI:10.1007/s00039-025-00701-5

Paul Bourgade, Patrick Lopatto, Ofer Zeitouni

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引用次数: 0

摘要

我们确定了Wigner矩阵和β-系综的特征多项式的极大值的导阶。在高斯可整除Wigner矩阵的特殊情况下，我们的方法提供了最大值到紧性的通用性。这是关于这些模型的Fyodorov-Hiary-Keating猜想的第一个普遍结果，特别是回答了Wigner矩阵谱的最优刚性问题。我们的证明将特征值统计的普适性的动态技术与对数相关场的最大值和高斯乘法混沌的思想结合起来。

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Optimal Rigidity and Maximum of the Characteristic Polynomial of Wigner Matrices

We determine to leading order the maximum of the characteristic polynomial for Wigner matrices and β-ensembles. In the special case of Gaussian-divisible Wigner matrices, our method provides universality of the maximum up to tightness. These are the first universal results on the Fyodorov–Hiary–Keating conjectures for these models, and in particular answer the question of optimal rigidity for the spectrum of Wigner matrices.

Our proofs combine dynamical techniques for universality of eigenvalue statistics with ideas surrounding the maxima of log-correlated fields and Gaussian multiplicative chaos.

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来源期刊

Geometric and Functional Analysis 数学-数学

CiteScore

3.70

自引率

4.50%

发文量

审稿时长

6-12 weeks

期刊介绍： Geometric And Functional Analysis (GAFA) publishes original research papers of the highest quality on a broad range of mathematical topics related to geometry and analysis. GAFA scored in Scopus as best journal in "Geometry and Topology" since 2014 and as best journal in "Analysis" since 2016. Publishes major results on topics in geometry and analysis. Features papers which make connections between relevant fields and their applications to other areas.