Salvato in:
| Autore principale: | |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| Soggetti: | |
| Accesso online: | https://arxiv.org/abs/2511.22731 |
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Sommario:
- We study random covers of a closed hyperbolic surface $Σ$, subject to the condition that, for $k\geq 2$, the fundamental group is isomorphic to the free group $F_k$. We show that asymptotically they distribute according to a specific probability measure on the moduli space of metric graphs. As we will demonstrate with explicit calculations for $k=2$, this allows us to determine asymptotic values for the expectation of the systole and other geometric invariants of the covers.