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Title:
Statistical regularities of self-intersections for geodesics on hyperbolic surfaces: local geometric properties
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Abstract:
In joint work with S. Lalley, J. Sapir, and M. Wroten, we show that the tessellation of a compact, hyperbolic 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. This work is inspired by the work of Chas and Chas-Lalley.
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