Random covers of surfaces

Sophie Wright

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arXiv · 2511.22731

Random covers of surfaces

Sophie Wright

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Abstract

We study random covers of a closed hyperbolic surface $\Sigma$, 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.

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BibTeX RIS

Sophie Wright. 2025-11-27. Random covers of surfaces. https://arxiv.org/abs/2511.22731

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