A Random Matrix Decimation Procedure Relating beta=2/(r 1) to beta=2(r 1)
Peter J Forrester
COMMUNICATIONS IN MATHEMATICAL PHYSICS | SPRINGER | Published : 2009
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 an..View full abstract
The idea of seeking inter-relations of the type reported on here is due to Balint Virag, communicated to the author at the AMS-IMS-SIAM summer research conference on Random Matrix Theory, Integrable Systems, and Stochastic Processes (June, 2007). This work has been supported by the Australian Research Council.