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A note on the Pfaffian integration theorem

Alexei Borodin et al 2007 J. Phys. A: Math. Theor. 40 F849-F855   doi: 10.1088/1751-8113/40/36/F01  Help

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Alexei Borodin1 and Eugene Kanzieper2
1 Department of Mathematics, California Institute of Technology, CA 91125, USA
2 Department of Applied Mathematics, H.I.T.–Holon Institute of Technology, Holon 58102, Israel
E-mail: borodin@caltech.edu and eugene.kanzieper@weizmann.ac.il

Abstract. 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 numbers: 02.10.Yn, 02.50.−r, 05.40.−a

Print publication: Issue 36 (7 September 2007)
Received 18 July 2007, in final form 31 July 2007
Published 21 August 2007

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