Local universality of determinantal point processes on Riemannian manifolds (Q2679703)

Let \(\mathcal X_\lambda\) be the determinantal point process for the spectral projection of the Laplacian on a compact Riemannian manifold \(M\) up to \(\lambda^2\). It is proved that under a suitable scaling, the pull-back of \(\mathcal X_\lambda\) under the exponential map from \(T_p^*M\) to \(M\) converges weakly to the universal determinantal point process as \(\lambda\to \infty.\)