Abstract
The Lame polynomials naturally arise when separating variables in Laplace's equation in elliptic coordinates. The products of these polynomials form a class of spherical harmonics, which are joint eigenfunctions of a quantum completely integrable (QCI) system of commuting, second-order differential operators P0=Δ, P1,…,PN−1 acting on C∞(?N). These operators naturally depend on parameters and thus constitute an ensemble. In this paper, we compute the limiting level-spacings distributions for the zeroes of the Lame polynomials in various thermodynamic, asymptotic regimes. We give results both in the mean and pointwise, for an asymptotically full set of values of the parameters.
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