Poissonian pair correlation on manifolds via the heat kernel
arXiv:1904.08286
Abstract
We define a notion of Poissonian pair correlation (PPC) for Riemannian manifolds without boundary and prove that PPC implies uniform distribution in this setting. This extends earlier work by Grepstad and Larcher, Aistleitner, Lachmann, and Pausinger, Steinerberger, and Marklof.
There is a serious mistake in the proof of Proposition 1