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Counting statistics for geodesics on flat surfaces

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arxiv 2503.13091 v1 pith:55UBELPD submitted 2025-03-17 math.DS math.GTmath.PR

Stephen Cantrell , Mark Pollicott This is my paper · ORCID
classification math.DSmath.GTmath.PR
keywords countingflatlengthsurfacesapplycomparecomparisonfunctions
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We study counting limit laws that compare length functions on infinite graphs. We then apply these results to flat surfaces to obtain a statistical comparison between the geometric length and the number of singularities visited by geodesic paths.

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Cited by 1 Pith paper

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  1. Quasi-geodesics in the Cannon-Thurston metric

    math.GT 2025-10 conditional novelty 7.0 of 10

    Surface-side random measures pushed through the Cannon–Thurston map are mutually singular with every natural 3-manifold measure on the boundary sphere of a fibered hyperbolic 3-manifold, with exponential effective rates.

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