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A Random Matrix Decimation Procedure Relating β = 2/(r + 1) to β =  2(r + 1)

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Abstract

Classical random matrix ensembles with orthogonal symmetry have the property that the joint distribution of every second eigenvalue is equal to that of a classical random matrix ensemble with symplectic symmetry. These results are shown to be the case r = 1 of a family of inter-relations between eigenvalue probability density functions for generalizations of the classical random matrix ensembles referred to as β-ensembles. The inter-relations give that the joint distribution of every (r + 1)st eigenvalue in certain β-ensembles with β  =  2/(r + 1) is equal to that of another β-ensemble with β  =  2(r + 1). The proof requires generalizing a conditional probability density function due to Dixon and Anderson.

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Authors and Affiliations

  1. Department of Mathematics and Statistics, University of Melbourne, Victoria, 3010, Australia

    Peter J. Forrester

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  1. Peter J. Forrester
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Correspondence to Peter J. Forrester.

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Communicated by P. Sarnak

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Forrester, P.J. A Random Matrix Decimation Procedure Relating β = 2/(r + 1) to β =  2(r + 1). Commun. Math. Phys. 285, 653–672 (2009). https://doi.org/10.1007/s00220-008-0616-0

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  • DOI: https://doi.org/10.1007/s00220-008-0616-0

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