Commutators of random matrices from the unitary and orthogonal groups

被引：0

作者：

Palheta, Pedro H. S. ^{[1
]}

Barbosa, Marcelo R. ^{[1
]}

Novaes, Marcel ^{[1
]}

机构：

[1] Univ Fed Uberlandia, Inst Fis, BR-38408100 Uberlandia, Brazil

来源：

JOURNAL OF MATHEMATICAL PHYSICS | 2022年 / 63卷 / 11期

关键词：

STATISTICAL-THEORY; ENERGY-LEVELS; IRREDUCIBLE REPRESENTATIONS; 2ND-ORDER FREENESS; GROUP INTEGRALS; CHARACTERS; FLUCTUATIONS; ASYMPTOTICS; EIGENVALUES; PRODUCTS;

D O I：

10.1063/5.0041240

中图分类号：

O4 [物理学];

学科分类号：

0702 ;

摘要：

We investigate the statistical properties of C = uvu(-1)v(-1), when u and v are independent random matrices, uniformly distributed with respect to the Haar measure of the groups U(N) and O(N). An exact formula is derived for the average value of power sum symmetric functions of C, and also for products of the matrix elements of C, similar to Weingarten functions. The density of eigenvalues of C is shown to become constant in the large-N limit, and the first N-1 correction is found. Published under an exclusive license by AIP Publishing.

引用

页数：17

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