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International Mathematics Research Notices (2007) Vol. 2007 : article ID rnm015, 15 page, doi:10.1093/imrn/rnm015 published on May 24, 2007
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Copyright © The Author 2007. Published by Oxford University Press.

Averages over Ginibre's Ensemble of Random Real Matrices

Christopher D. Sinclair

Pacific Institute for the Mathematical Sciences, Vancouver, British Columbia

Correspondence: Correspondence to be sent to: sinclair{at}math.ubc.ca

We give a formula for computing the ensemble average of multiplicative class functions over the Gaussian ensemble of real asymmetric matrices. This formula allows ensemble averages to be written as the Pfaffian of Gram-like antisymmetric matrices formed with respect to a skew-symmetric inner product related to the class function.

Communicated by Alexei Borodin


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