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THE SIMPLE SEPARATING SYSTOLE FOR HYPERBOLIC SURFACES OF LARGE GENUS

Published online by Cambridge University Press:  31 May 2021

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])

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.

Type
Research Article
Copyright
© The Author(s), 2021. Published by Cambridge University Press

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