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arXiv · 2312.10517

Length spectrum of large genus random metric maps

Simon Barazer·Alessandro Giacchetto·Mingkun Liu
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Abstract

We study the length of short cycles on uniformly random metric maps (also known as ribbon graphs) of large genus using a Teichm\"uller theory approach. We establish that, as the genus tends to infinity, the length spectrum converges to a Poisson point process with an explicit intensity. This result extends the work of Janson and Louf to the multi-faced case.

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Simon Barazer, Alessandro Giacchetto, Mingkun Liu. 2023-12-16. Length spectrum of large genus random metric maps. https://doi.org/10.1017/fms.2025.31

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