Product of random projections, Jacobi ensembles and universality problems arising from free probability

被引：75
作者：
Collins, B [1 ]
机构：
[1] Kyoto Univ, Grad Sch Sci, Dept Math, Sakyo Ku, Kyoto 6068502, Japan
来源：
PROBABILITY THEORY AND RELATED FIELDS | 2005年 / 133卷 / 03期
关键词：
Correlation Function; Stochastic Process; Probability Theory; Mathematical Biology; Local Property;
D O I：
10.1007/s00440-005-0428-5
中图分类号：
O21 [概率论与数理统计]; C8 [统计学];
学科分类号：
020208 ; 070103 ; 0714 ;
摘要：
We consider the product of two independent randomly rotated projectors. The square of its radial part turns out to be distributed as a Jacobi ensemble. We study its global and local properties in the large dimension scaling relevant to free probability theory. We establish asymptotics for one point and two point correlation functions, as well as properties of largest and smallest eigenvalues.
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收藏
页码：315 / 344
页数：30
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