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We consider the nth-order spacing distribution, Pⁿ(s), in the statistical theory of energy levels of complex systems. Each Pⁿ is written as a sum of multiple integrals over correlation functions. This procedure is used to establish the identity of the spacing distributions for all members of a class of Hamiltonian unitary ensembles. A power-series expansion of Pⁿ(s), valid for all n, is developed.
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Fox et al. (1964) studied this question.
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