Local geometry of random geodesics on negatively curved surfaces
Annales Henri Lebesgue, Volume 4 (2021) , pp. 187-226.

Keywordsself-intersection, random tessellation, geodesic, hyperbolic surface, Poisson line process

### Abstract

We show that the tessellation of a compact, negatively curved surface induced by a long random 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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