随机矩阵的普适性与局部松弛流
数学物理
2010-11-25 v5 math.MP
摘要
我们考虑 对称随机矩阵，其中每个矩阵元素的概率分布由具有次指数衰减的测度 给出。我们证明，在 极限下，这些矩阵与高斯正交系综（GOE）在谱内部的能级间距统计量相同。我们的方法基于对戴森布朗运动的研究，通过一种相关的新动力学——局部松弛流来实现。
引用
@article{arxiv.0907.5605,
title = {Universality of Random Matrices and Local Relaxation Flow},
author = {Laszlo Erdos and Benjamin Schlein and Horng-Tzer Yau},
journal= {arXiv preprint arXiv:0907.5605},
year = {2010}
}
备注
A minor error in the proof of Lemma 2.2 has been corrected and an additional technical condition was added to Cor. 2.4. Final version with some more details in Prop 4.1 was added on Nov 24