大型变形酉不变模型谱中的离群值
概率论
2015-03-23 v2 算子代数
摘要
本文刻画了大型变形酉不变加法和乘法模型谱中可能的离群值及其对应的特征向量。我们允许未变形的酉不变模型和扰动矩阵在其谱中具有非平凡的极限谱测度和尖峰离群值。我们揭示了一个显著的新现象：单个尖峰可以在变形模型的谱中渐近地产生多个离群值。自由从属函数在这一分析中起着关键作用。
引用
@article{arxiv.1412.4916,
title = {Outliers in the spectrum of large deformed unitarily invariant models},
author = {Serban Teodor Belinschi and Hari Bercovici and Mireille Capitaine and Maxime Fevrier},
journal= {arXiv preprint arXiv:1412.4916},
year = {2015}
}
备注
44 pages, LaTeX, one figure. Several changes form the previous version, including a correction in Lemma 3.1 and the addition of several remarks and of a numerical example, kindly provided by Charles Bordenave. Same title as arXiv:1207.5443, which it greatly expands