算子值酉随机矩阵及其渐近自由性

数学物理学报

算子值酉随机矩阵及其渐近自由性

孟彬;郭懋正;曹小红

南京航空航天大学理学院南京 210016; 北京大学数学科学学院北京100871

收稿日期:2005-11-01 修回日期:2006-08-03 出版日期:2007-10-25 发布日期:2007-10-25
通讯作者: 孟彬
基金资助:
南航创新基金(1008-905711)资助

Operator-Valued Unitary Random Matrices and Asymptotic Freeness

Meng Bin;Guo Maozheng;Cao Xiaohong

College of Science, Nanjing University of Aeronautics and Astronautics, Nanjing 210016;

School of Mathematical Science, Peking University, Beijing 100871

Received:2005-11-01 Revised:2006-08-03 Online:2007-10-25 Published:2007-10-25
Contact: Meng Bin

摘要/Abstract

摘要： 该文在算子值非交换概率空间上引入半标准酉随机矩阵的概念, 证明了它是算子值Haar酉元的矩阵模型,并给出了半标准酉随机矩阵的渐近自由判定定理.

关键词: 算子值非交换概率空间, 半标准算子值酉随机矩阵, 渐近自由

Abstract: In this paper a notion of semi-standard unitary random matrix is introduced in operator-valued noncommutative probability space and the semi-standard unitary random matrices to be the asymptotic free matrix models for operator-valued Haar unitary elements is proved.

Key words: Operator-valued noncommutative probability space, Semi-standard unitary random matrix, Asymptotic freeness

中图分类号:

46L09

孟彬;郭懋正;曹小红. 算子值酉随机矩阵及其渐近自由性[J]. 数学物理学报, 2007, 27(5): 915-922.

Meng Bin;Guo Maozheng;Cao Xiaohong. Operator-Valued Unitary Random Matrices and Asymptotic Freeness[J]. Acta mathematica scientia,Series A, 2007, 27(5): 915-922.