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A note on the Pfaffian integration theorem

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Alexei Borodin1 and Eugene Kanzieper2

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Two alternative, fairly compact proofs are presented of the Pfaffian integration theorem that surfaced in the recent studies of spectral properties of Ginibre's Orthogonal Ensemble. The first proof is based on a concept of the Fredholm Pfaffian; the second proof is purely linear algebraic.


PACS

02.10.Yn Matrix theory

02.10.Ud Linear algebra

02.30.Cj Measure and integration

MSC

28Axx Classical measure theory

15A52 Random matrices

Subjects

Mathematical physics

Dates

Issue 36 (7 September 2007)

Received 18 July 2007, in final form 31 July 2007

Published 21 August 2007



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