Counting statistics for geodesics on flat surfaces

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.

Publication Details

Journal
ArXiv.org
Published
2025-03-17
Primary Topic
Stochastic processes and statistical mechanics
Type
article
Field-Weighted Citation Impact
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article

Counting statistics for geodesics on flat surfaces

ArXiv.org
Stochastic processes and statistical mechanics
article

Counting statistics for geodesics on flat surfaces

article en

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.

ArXiv.org
Openalex Percentile: Top 44%
Stochastic processes and statistical mechanics
Open Access PDFOpenAlex
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Counting statistics for geodesics on flat surfaces · ArXiv.org (2025) | TGRS Research Map | TGRS