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arXiv · 1904.08286

Poissonian pair correlation on manifolds via the heat kernel

Peter J. Grabner·Tetiana A. Stepanyuk
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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.

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Peter J. Grabner, Tetiana A. Stepanyuk. 2019-04-17. Poissonian pair correlation on manifolds via the heat kernel. https://arxiv.org/abs/1904.08286

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