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The diameter of random Belyi surfaces

Abstract : We determine the asymptotic growth rate of the diameter of the random hyperbolic surfaces constructed by Brooks and Makover (J. Differential Geom. 68 (2004) 121–157). This model consists of a uniform gluing of 2n hyperbolic ideal triangles along their sides followed by a compactification to get a random hyperbolic surface of genus roughly n2. We show that the diameter of those random surfaces is asymptotic to 2logn in probability as n→∞.
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Preprints, Working Papers, ...
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https://hal-universite-paris-saclay.archives-ouvertes.fr/hal-03287264
Contributor : Nicolas CURIEN Connect in order to contact the contributor
Submitted on : Thursday, July 15, 2021 - 3:03:54 PM
Last modification on : Friday, August 5, 2022 - 11:59:58 AM

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Thomas Budzinski, Nicolas Curien, Bram Petri. The diameter of random Belyi surfaces. 2021. ⟨hal-03287264⟩

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