Length partition of random multicurves on large genus hyperbolic surfaces

  • Vincent Delecroix

    Université de Bordeaux, Talence, France
  • Mingkun Liu

    Université Paris Cité, Paris, France; Sorbonne Université, Paris, France
Length partition of random multicurves on large genus hyperbolic surfaces cover

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Abstract

We study the length statistics of the components of a random multicurve on a closed surface of genus at least 2. This investigation was initiated by Mirzakhani in a paper published in 2016 where she studied the case of random pants decompositions. We prove that as the genus tends to infinity these statistics converge in law to the Poisson–Dirichlet distribution with parameter 1/2. In particular, the mean lengths of the three longest components converge to 75.8%, 17.1% and 4.9% of the total length, respectively.

Cite this article

Vincent Delecroix, Mingkun Liu, Length partition of random multicurves on large genus hyperbolic surfaces. J. Eur. Math. Soc. (2024), published online first

DOI 10.4171/JEMS/1469