• Corpus ID: 232105075

Short cycles in high genus unicellular maps

@inproceedings{Janson2021ShortCI,
  title={Short cycles in high genus unicellular maps},
  author={Svante Janson and Baptiste Louf},
  year={2021}
}
We study large uniform random maps with one face whose genus grows linearly with the number of edges, which are a model of discrete hyperbolic geometry. In previous works, several hyperbolic geometric features have been investigated. In the present work, we study the number of short cycles in a uniform unicellular map of high genus, and we show that it converges to a Poisson distribution. As a corollary, we obtain the law of the systole of uniform unicellular maps in high genus. We also obtain… 
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Unicellular maps vs hyperbolic surfaces in large genus: simple closed curves
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