随机贝伊曲面的直径

arXiv: Geometric Topology Pub Date : 2019-10-25 DOI:10.2140/agt.2021.21.2929

Thomas Budzinski, N. Curien, Bram Petri

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引用次数: 8

摘要

我们确定了Brooks和Makover构造的随机双曲曲面直径的渐近增长率。该模型由$2n$双曲理想三角形沿其侧面的均匀胶合组成，然后进行紧化以获得一个大致为$n/2$的随机双曲曲面。我们证明了这些随机曲面的直径在概率上是渐近于$2 \log n$的，如$n \to \infty$。

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The diameter of random Belyi surfaces

We determine the asymptotic growth rate of the diameter of the random hyperbolic surfaces constructed by Brooks and Makover. 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 $n/2$. We show that the diameter of those random surfaces is asymptotic to $2 \log n$ in probability as $n \to \infty$.

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arXiv: Geometric Topology

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