Geodesic
Length spectrum of large genus random metric maps
Forum of Mathematics, Sigma, Tome 13 (2025) no. 1, p. e70

Voir la notice de l'article provenant de la source Cambridge University Press

We study the length of short cycles on uniformly random metric maps (also known as ribbon graphs) of large genus using a Teichmüller 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. 
Barazer, Simon; Giacchetto, Alessandro; Liu, Mingkun. Length spectrum of large genus random metric maps. Forum of Mathematics, Sigma, Tome 13 (2025) no. 1, p. e70. doi: 10.1017/fms.2025.31
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