Wigner随机矩阵谱边的普适性
数学物理
2009-10-31 v2 math.MP
概率论
摘要
我们证明了在极限下Wigner随机矩阵重标度相关函数在谱边的普适性。作为一个推论，我们表明，在适当重标度后，Wigner随机厄米（相应为实对称）矩阵的第一、第二、第三等本征值弱收敛于Tracy和Widom在G.U.E.（G.O.E.）情形下建立的分布。
引用
@article{arxiv.math-ph/9907013,
title = {Universality at the edge of the spectrum in Wigner random matrices},
author = {Alexander Soshnikov},
journal= {arXiv preprint arXiv:math-ph/9907013},
year = {2009}
}
备注
We corrected several misprints and little mistakes (the most important one is formula (1.15)). We also reformulated two auxiliary theorems (Theorem 2 and Theorem 3) to emphasize the asymptotic nature of the results