Counting statistics for geodesics on flat surfaces

2025/03/17 by Cantrell, Stephen, Pollicott, Mark
#Dynamical Systems (math.DS) #FOS: Mathematics #Geometric Topology (math.GT) #Probability (math.PR)

paper · doi:10.48550/arxiv.2503.13091

Abstract

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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