某些随机Vandermonde矩阵的渐近*-矩
概率论
2017-07-25 v2 算子代数
摘要
研究了基于单位圆上均匀分布的独立随机变量的适当归一化平方随机Vandermonde矩阵。结果表明，随着矩阵大小无限增大，关于迹的期望存在渐近*-分布，等于一个C[0,1]值R-对角元的*-分布。
引用
@article{arxiv.1602.02815,
title = {Asymptotic *-moments of some random Vandermonde matrices},
author = {March Boedihardjo and Ken Dykema},
journal= {arXiv preprint arXiv:1602.02815},
year = {2017}
}
备注
35 pages. Mathematica file available in consideration of computations of certain noncrossing cumulants. In version 1, Remark 2.1 was incorrect. This is corrected in version 2, where it is now Lemma 2.1. The proofs of Proposition 2.2 and several results in Section 4 were modified accordingly. Statements of these results remain the same, though they appear in different order