Filling random cycles
Metric Geometry
2021-11-29 v2 Probability
Abstract
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--Koml\'os--Tusn\'ady 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 random geometric objects.
Cite
@article{arxiv.2008.10761,
title = {Filling random cycles},
author = {Fedor Manin},
journal= {arXiv preprint arXiv:2008.10761},
year = {2021}
}
Comments
23 pages, 1 figure. Version 2 improves the exposition and fixes careless errors and sloppiness; no changes to (intended) mathematical content