Open Access
2009 Duality of real and quaternionic random matrices
Wlodek Bryc, Virgil Pierce
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Electron. J. Probab. 14: 452-476 (2009). DOI: 10.1214/EJP.v14-606


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.


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Wlodek Bryc. Virgil Pierce. "Duality of real and quaternionic random matrices." Electron. J. Probab. 14 452 - 476, 2009.


Accepted: 10 February 2009; Published: 2009
First available in Project Euclid: 1 June 2016

zbMATH: 1188.15034
MathSciNet: MR2480549
Digital Object Identifier: 10.1214/EJP.v14-606

Primary: 15A52
Secondary: 05A15 , 60G15

Keywords: Euler characteristic , Gaussian Symplectic Ensemble , Mobius graphs , moments , quaternion Wishart

Vol.14 • 2009
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