The rescaled distance between random points in high-genus triangulations converges in probability to a deterministic constant.
A sharper bound on the minimal possible diameter of a closed hyperbolic surface
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abstract
We prove that the minimal possible diameter of a closed hyperbolic surface of genus $g$ is at most $\log(g)+25 \log \log(g) + O(1)$.
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math.PR 1years
2026 1verdicts
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Typical distances in high-genus triangulations
The rescaled distance between random points in high-genus triangulations converges in probability to a deterministic constant.