Length partition of random multicurves on large genus hyperbolic surfaces

Delecroix Vincent; Liu Mingkun

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arXiv · 2202.10255

Length partition of random multicurves on large genus hyperbolic surfaces

Delecroix Vincent·Liu Mingkun

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Abstract

We study the length statistics of the components of a random multicurve on a surface of genus $g \geq 2$. For each fixed genus, the existence of such statistics follows from the work of M.~Mirzakhani, F.~Arana-Herrera and M.~Liu. We prove that as the genus $g$ tends to infinity the statistics converge in law to the Poisson--Dirichlet distribution of parameter $\theta=1/2$. In particular, as the genus tends to infinity the mean length of the three longest components converge respectively to $75.8\%$, $17.1\%$ and $4.9\%$ of the total length.

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BibTeX RIS

Delecroix Vincent, Liu Mingkun. 2022-02-21. Length partition of random multicurves on large genus hyperbolic surfaces. https://arxiv.org/abs/2202.10255

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