Higher Order Spacing Distributions for a Class of Unitary Ensembles

Abstract

We consider the $n\mathrm{th}$-order spacing distribution, ${P}^{n}(s)$, in the statistical theory of energy levels of complex systems. Each ${P}^{n}$ 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 ${P}^{n}(s)$, valid for all $n$, is developed.