Duality of real and quaternionic random matrices

被引：9

作者：

Bryc, Wlodzimierz ^{[1
]}

Pierce, Virgil ^{[2
]}

机构：

[1] Univ Cincinnati, Dept Math Sci, Cincinnati, OH 45221 USA

[2] UT Pan Amer, Dept Math, Edinburg, TX 78539 USA

来源：

ELECTRONIC JOURNAL OF PROBABILITY | 2009年 / 14卷

基金：

美国国家科学基金会;

关键词：

Gaussian Symplectic Ensemble; quaternion Wishart; moments; Mobius graphs; Euler characteristic; LOCALLY ORIENTABLE SURFACES; MAPS;

D O I：

10.1214/EJP.v14-606

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 show that quaternionic Gaussian random variables satisfy a generalization of the Wick formula for computing the expected value of products in terms of a family of graphical enumeration problems. When applied to the quaternionic Wigner and Wishart families of random matrices the result gives the duality between moments of these families and the corresponding real Wigner and Wishart families.

引用

页码：452 / 476

页数：25

共 28 条

[1] [Anonymous], 1997, Cambridge Tracts in Mathematics
[2] [Anonymous], 1998, J HIGH ENERGY PHYS
[3] Bessis D., 1980, ADV APPL MATH, V1, P109, DOI [DOI 10.1016/0196-8858, 10.1016/0196-8858(80)90008-1]
[4] BESSIS D, 1980, ADV APPL MATH, V2, P109
[5] Compound Real Wishart and q-Wishart Matrices
Bryc, Wlodzimierz
[J]. INTERNATIONAL MATHEMATICS RESEARCH NOTICES, 2008, 2008
[6] Global spectrum fluctuations for the β-Hermite and β-Laguerre ensembles via matrix models
Dumitriu, Ioana
Edelman, Alan
[J]. JOURNAL OF MATHEMATICAL PHYSICS, 2006, 47 (06)
[7] Ercolani NM, 2003, INT MATH RES NOTICES, V2003, P755
[8] Maps in locally orientable surfaces, the double coset algebra, and zonal polynomials
Goulden, IP
Jackson, DM
[J]. CANADIAN JOURNAL OF MATHEMATICS-JOURNAL CANADIEN DE MATHEMATIQUES, 1996, 48 (03): : 569 - 584
[9] Maps in locally orientable surfaces and integrals over real symmetric surfaces
Goulden, IP
Jackson, DM
[J]. CANADIAN JOURNAL OF MATHEMATICS-JOURNAL CANADIEN DE MATHEMATIQUES, 1997, 49 (05): : 865 - 882
[10] Connection coefficients, matchings, maps and combinatorial conjectures for Jack symmetric functions
Goulden, IP
Jackson, DM
[J]. TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY, 1996, 348 (03) : 873 - 892

← 1 2 3 →