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- W4287932007 abstract "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 the asymptotic distribution of the vertex degrees in such a map." @default.
- W4287932007 created "2022-07-26" @default.
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- W4287932007 date "2021-03-03" @default.
- W4287932007 modified "2023-09-29" @default.
- W4287932007 title "Short cycles in high genus unicellular maps" @default.
- W4287932007 doi "https://doi.org/10.48550/arxiv.2103.02549" @default.
- W4287932007 hasPublicationYear "2021" @default.
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