Filling random cycles

@article{Manin2021FillingRC,
  title={Filling random cycles},
  author={Fedor Manin},
  journal={Commentarii Mathematici Helvetici},
  year={2021}
}
  • Fedor Manin
  • Published 25 August 2020
  • Mathematics
  • Commentarii Mathematici Helvetici
We compute the asymptotic behavior of the average-case filling volume for certain models of random Lipschitz cycles in the unit cube and sphere. For example, we estimate the minimal area of a Seifert surface for a model of random knots first studied by Millett. This is a generalization of the classical Ajtai--Komlos--Tusnady optimal matching theorem from combinatorial probability. The author hopes for applications to the topology of random links, random maps between spheres, and other models of… 

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