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 |
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Hauptverfasser: | , |
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. |
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ISSN: | 0022-4715 1572-9613 |
DOI: | 10.1007/s10955-009-9684-6 |