A Method to Calculate Correlation Functions for β=1 Random Matrices of Odd Size

The calculation of correlation functions for β =1 random matrix ensembles, which can be carried out using Pfaffians, has the peculiar feature of requiring a separate calculation depending on the parity of the matrix size N . This same complication is present in the calculation of the correlations fo...

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Veröffentlicht in:Journal of statistical physics 2009-02, Vol.134 (3), p.443-462
Hauptverfasser: Forrester, Peter J., Mays, Anthony
Format: Artikel
Sprache:eng
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Zusammenfassung:The calculation of correlation functions for β =1 random matrix ensembles, which can be carried out using Pfaffians, has the peculiar feature of requiring a separate calculation depending on the parity of the matrix size N . This same complication is present in the calculation of the correlations for the Ginibre Orthogonal Ensemble of real Gaussian matrices. In fact the methods used to compute the β =1, N odd, correlations break down in the case of N odd real Ginibre matrices, necessitating a new approach to both problems. The new approach taken in this work is to deduce the β =1, N odd correlations as limiting cases of their N even counterparts, when one of the particles is removed towards infinity. This method is shown to yield the correlations for N odd real Gaussian matrices.
ISSN:0022-4715
1572-9613
DOI:10.1007/s10955-009-9684-6