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THE SIMPLE SEPARATING SYSTOLE FOR HYPERBOLIC SURFACES OF LARGE GENUS

Part of: Low-dimensional topology Deformations of analytic structures

Published online by Cambridge University Press:  31 May 2021

Hugo Parlier ,
Yunhui Wu  and
Yuhao Xue Open the ORCID record for Yuhao Xue [Opens in a new window]
Hugo Parlier
Affiliation:
Department of Mathematics, University of Luxembourg, Esch-sur-Alzette, Luxembourg ([email protected])
Yunhui Wu
Affiliation:
Yau Mathematical Sciences Center & Department of Mathematical Sciences, Tsinghua University, Beijing, China ([email protected]); ([email protected])
Yuhao Xue
Affiliation:
Yau Mathematical Sciences Center & Department of Mathematical Sciences, Tsinghua University, Beijing, China ([email protected]); ([email protected])
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Abstract

In this note we show that the expected value of the separating systole of a random surface of genus g with respect to Weil–Petersson volume behaves like $2\log g $ as the genus goes to infinity. This is in strong contrast to the behavior of the expected value of the systole which, by results of Mirzakhani and Petri, is independent of genus.

Keywords

Random surfacesSimple separating systoleWeil-Petersson volumes

MSC classification

Primary: 32G15: Moduli of Riemann surfaces, Teichmüller theory
Secondary: 57M50: Geometric structures on low-dimensional manifolds
Type
Research Article
Information
Journal of the Institute of Mathematics of Jussieu , Volume 21 , Issue 6 , November 2022 , pp. 2205 - 2214
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Copyright
© The Author(s), 2021. Published by Cambridge University Press

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