Local universality of determinantal point processes on Riemannian manifolds.

We consider the Laplace-Beltrami operator Δg on a smooth, compact Riemannian manifold (M,g) and the determinantal point process χλ on M associated with the spectral projection of -Δg onto the subspace corresponding to the eigenvalues up to λ². We show that the pull-back of χλ by the exponential map expp: Tp*M → M under a suitable scaling converges weakly to the universal determinantal point process on Tp*M as λ→∞. [ABSTRACT FROM AUTHOR]