Optimal decay of eigenvector overlap for non-Hermitian random matrices

IF 1.6 2区数学 Q1 MATHEMATICS

Journal of Functional Analysis Pub Date : 2025-09-01 DOI:10.1016/j.jfa.2025.111180

Giorgio Cipolloni , László Erdős , Yuanyuan Xu

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引用次数: 0

Abstract

We consider the standard overlap

O_{i j} : = 〈 r_{j}, r_{i} 〉 〈 l_{j}, l_{i} 〉

of any bi-orthogonal family of left and right eigenvectors of a large random matrix X with centred i.i.d. entries and we prove that it decays as an inverse second power of the distance between the corresponding eigenvalues. This extends similar results for the complex Gaussian ensemble from Bourgade and Dubach [15], as well as Benaych-Georges and Zeitouni [13], to any i.i.d. matrix ensemble in both symmetry classes. As a main tool, we prove a two-resolvent local law for the Hermitisation of X uniformly in the spectrum with optimal decay rate and optimal dependence on the density near the spectral edge.

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非厄米随机矩阵特征向量重叠的最优衰减

我们考虑一个大随机矩阵X的任意双正交的左右特征向量族的标准重叠Oij:= < rj,ri > < lj,li >，我们证明了它衰减为对应特征值之间距离的倒数次幂。这将复高斯系综的类似结果从Bourgade和Dubach[15]，以及Benaych-Georges和Zeitouni[13]推广到两种对称类中的任何i.i.d矩阵系综。作为一种主要工具，我们证明了X在光谱中均匀地具有最佳衰减率和最优依赖于谱边附近密度的双解局域律。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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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