Local geometry of random geodesics on negatively curved surfaces

Jayadev S. Athreya; Steven P. Lalley; Jenya Sapir; Matthew Wroten

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arXiv · 1708.09830

Local geometry of random geodesics on negatively curved surfaces

Jayadev S. Athreya·Steven P. Lalley·Jenya Sapir·Matthew Wroten

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Abstract

It is shown that the tessellation of a compact, negatively curved surface induced by a typical long geodesic segment, when properly scaled, looks locally like a Poisson line process. This implies that the global statistics of the tessellation -- for instance, the fraction of triangles -- approach those of the limiting Poisson line process.

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BibTeX RIS

Jayadev S. Athreya, Steven P. Lalley, Jenya Sapir, Matthew Wroten. 2020-02-25. Local geometry of random geodesics on negatively curved surfaces. https://arxiv.org/abs/1708.09830

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