Inter-relationships between spacing distributions in random matrix theory
by Professor Peter Forrester
Abstract: In random matrix theory there is a parameter b which controls the level repulsion between neighbouring eigenvalues. It has been known since the pioneering work of Dyson and Mehta in the early 60s that integrating over every second eigenvalue in a b = 1 ensemble gives a b = 4 ensemble, while superimposing two b = 1 ensembles then integrating over every second eigenvalue gives a b = 2 ensemble. The implications of these results will be discussed for their consequences to spacing distributions, and a generalization will be given, which in turn relies on a generalization of the Dixon-Anderson integral from the theory of the Selberg integral.
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