论文标题
随机带和具有相关条目的块矩阵
Random Band and Block Matrices with Correlated Entries
论文作者
论文摘要
在本文中，我们得出了随机频带和带有相关条目的随机型矩阵的经验光谱分布的极限定律。在本文的第一部分中，我们研究带有大约不相关条目的频带矩阵。我们加强了先前获得的结果，同时需要较弱的假设，这是通过矩的精制应用来实现的。在本文的第二部分中，我们引入了一种我们称为SSB-HKW相关的新的两层相关结构，该结构可以研究具有相关条目的结构化随机矩阵。我们的结果包括概率和几乎可以肯定的半圆定律，但我们还根据条件获得了其他限制频谱分布。提供了简单的必要条件，使极限定律成为半圆。我们的发现增强并扩展了许多已经知道的结果。
In this paper, we derive limit laws for the empirical spectral distributions of random band and block matrices with correlated entries. In the first part of the paper, we study band matrices with approximately uncorrelated entries. We strengthen previously obtained results while requiring weaker assumptions, which is made possible by a refined application of the method of moments. In the second part of the paper, we introduce a new two-layered correlation structure we call SSB-HKW correlated, which enables the study of structured random matrices with correlated entries. Our results include semicircle laws in probability and almost surely, but we also obtain other limiting spectral distributions depending on the conditions. Simple necessary and sufficient conditions for the limit law to be the semicircle are provided. Our findings strengthen and extend many results already known.
