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Recursions and asymptotics of intersection numbers

Kefeng Liu Motohico Mulase Hao Xu

Algebraic Geometry mathscidoc:1912.43117

International Journal of Mathematics, 27, (9), 1650072, 2016.8
We establish the asymptotic expansion of certain integrals of classes on moduli spaces of curves , when either the or goes to infinity. Our main tools are cut-join type recursion formulae from the WittenKontsevich theorem, as well as asymptotics of solutions to the first Painlev equation. We also raise a conjecture on large genus asymptotics for -point functions of classes and partially verify the positivity of coefficients in generalized Mirzakhanis formula of higher WeilPetersson volumes.
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@inproceedings{kefeng2016recursions,
  title={Recursions and asymptotics of intersection numbers},
  author={Kefeng Liu, Motohico Mulase, and Hao Xu},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20191221111637111965677},
  booktitle={International Journal of Mathematics},
  volume={27},
  number={9},
  pages={1650072},
  year={2016},
}
Kefeng Liu, Motohico Mulase, and Hao Xu. Recursions and asymptotics of intersection numbers. 2016. Vol. 27. In International Journal of Mathematics. pp.1650072. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20191221111637111965677.
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